diff --git a/source/api_c/include/deepmd.hpp b/source/api_c/include/deepmd.hpp
index 4a376e0bec..503a4c4b4b 100644
--- a/source/api_c/include/deepmd.hpp
+++ b/source/api_c/include/deepmd.hpp
@@ -644,8 +644,8 @@ class DeepPot {
     const VALUETYPE *box_ = !box.empty() ? &box[0] : nullptr;
     const int *atype_ = &atype[0];
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     std::vector<VALUETYPE> fparam_, aparam_;
@@ -706,10 +706,10 @@ class DeepPot {
     const int *atype_ = &atype[0];
 
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
-    atom_energy.resize(nframes * natoms);
-    atom_virial.resize(nframes * natoms * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
+    atom_energy.resize(static_cast<size_t>(nframes) * natoms);
+    atom_virial.resize(static_cast<size_t>(nframes) * natoms * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     VALUETYPE *atomic_ener_ = &atom_energy[0];
@@ -774,8 +774,8 @@ class DeepPot {
     const VALUETYPE *box_ = !box.empty() ? &box[0] : nullptr;
     const int *atype_ = &atype[0];
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     std::vector<VALUETYPE> fparam_, aparam_;
@@ -845,10 +845,10 @@ class DeepPot {
     const int *atype_ = &atype[0];
 
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
-    atom_energy.resize(nframes * natoms);
-    atom_virial.resize(nframes * natoms * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
+    atom_energy.resize(static_cast<size_t>(nframes) * natoms);
+    atom_virial.resize(static_cast<size_t>(nframes) * natoms * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     VALUETYPE *atomic_ener_ = &atom_energy[0];
@@ -910,8 +910,8 @@ class DeepPot {
     const VALUETYPE *box_ = !box.empty() ? &box[0] : nullptr;
     const int *atype_ = &atype[0];
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     std::vector<VALUETYPE> fparam_, aparam_;
@@ -972,10 +972,10 @@ class DeepPot {
     const int *atype_ = &atype[0];
 
     double *ener_ = _DP_Get_Energy_Pointer(ener, nframes);
-    force.resize(nframes * natoms * 3);
-    virial.resize(nframes * 9);
-    atom_energy.resize(nframes * natoms);
-    atom_virial.resize(nframes * natoms * 9);
+    force.resize(static_cast<size_t>(nframes) * natoms * 3);
+    virial.resize(static_cast<size_t>(nframes) * 9);
+    atom_energy.resize(static_cast<size_t>(nframes) * natoms);
+    atom_virial.resize(static_cast<size_t>(nframes) * natoms * 9);
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
     VALUETYPE *atomic_ener_ = &atom_energy[0];
@@ -1079,7 +1079,7 @@ class DeepPot {
                           const int &dparam,
                           const std::vector<VALUETYPE> &param) const {
     if (param.size() == dparam) {
-      out_param.resize(nframes * dparam);
+      out_param.resize(static_cast<size_t>(nframes) * dparam);
       for (int ii = 0; ii < nframes; ++ii) {
         std::copy(param.begin(), param.end(), out_param.begin() + ii * dparam);
       }
@@ -1210,7 +1210,7 @@ class DeepPotModelDevi {
     virial.resize(numb_models);
     for (int i = 0; i < numb_models; i++) {
       ener[i] = energy_flat[i];
-      force[i].resize(natoms * 3);
+      force[i].resize(static_cast<size_t>(natoms) * 3);
       virial[i].resize(9);
       for (int j = 0; j < natoms * 3; j++) {
         force[i][j] = force_flat[i * natoms * 3 + j];
@@ -1292,10 +1292,10 @@ class DeepPotModelDevi {
     atom_virial.resize(numb_models);
     for (int i = 0; i < numb_models; i++) {
       ener[i] = energy_flat[i];
-      force[i].resize(natoms * 3);
+      force[i].resize(static_cast<size_t>(natoms) * 3);
       virial[i].resize(9);
       atom_energy[i].resize(natoms);
-      atom_virial[i].resize(natoms * 9);
+      atom_virial[i].resize(static_cast<size_t>(natoms) * 9);
       for (int j = 0; j < natoms * 3; j++) {
         force[i][j] = force_flat[i * natoms * 3 + j];
       }
@@ -1496,7 +1496,7 @@ class DeepPotModelDevi {
                           const int &dparam,
                           const std::vector<VALUETYPE> &param) const {
     if (param.size() == dparam) {
-      out_param.resize(nframes * dparam);
+      out_param.resize(static_cast<size_t>(nframes) * dparam);
       for (int ii = 0; ii < nframes; ++ii) {
         std::copy(param.begin(), param.end(), out_param.begin() + ii * dparam);
       }
@@ -1653,8 +1653,8 @@ class DeepTensor {
     const VALUETYPE *box_ = !box.empty() ? &box[0] : nullptr;
     const int *atype_ = &atype[0];
     global_tensor.resize(odim);
-    force.resize(odim * natoms * 3);
-    virial.resize(odim * 9);
+    force.resize(static_cast<size_t>(odim) * natoms * 3);
+    virial.resize(static_cast<size_t>(odim) * 9);
     VALUETYPE *global_tensor_ = &global_tensor[0];
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
@@ -1697,9 +1697,9 @@ class DeepTensor {
     const int *atype_ = &atype[0];
 
     global_tensor.resize(odim);
-    force.resize(odim * natoms * 3);
-    virial.resize(odim * 9);
-    atom_virial.resize(odim * natoms * 9);
+    force.resize(static_cast<size_t>(odim) * natoms * 3);
+    virial.resize(static_cast<size_t>(odim) * 9);
+    atom_virial.resize(static_cast<size_t>(odim) * natoms * 9);
     VALUETYPE *global_tensor_ = &global_tensor[0];
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
@@ -1752,8 +1752,8 @@ class DeepTensor {
     const VALUETYPE *box_ = !box.empty() ? &box[0] : nullptr;
     const int *atype_ = &atype[0];
     global_tensor.resize(odim);
-    force.resize(odim * natoms * 3);
-    virial.resize(odim * 9);
+    force.resize(static_cast<size_t>(odim) * natoms * 3);
+    virial.resize(static_cast<size_t>(odim) * 9);
     VALUETYPE *global_tensor_ = &global_tensor[0];
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
@@ -1800,9 +1800,9 @@ class DeepTensor {
     const int *atype_ = &atype[0];
 
     global_tensor.resize(odim);
-    force.resize(odim * natoms * 3);
-    virial.resize(odim * 9);
-    atom_virial.resize(odim * natoms * 9);
+    force.resize(static_cast<size_t>(odim) * natoms * 3);
+    virial.resize(static_cast<size_t>(odim) * 9);
+    atom_virial.resize(static_cast<size_t>(odim) * natoms * 9);
     VALUETYPE *global_tensor_ = &global_tensor[0];
     VALUETYPE *force_ = &force[0];
     VALUETYPE *virial_ = &virial[0];
@@ -1954,7 +1954,7 @@ class DipoleChargeModifier {
     const int *dpairs = reinterpret_cast<const int *>(&pairs[0]);
     const VALUETYPE *delef = &delef_[0];
 
-    dfcorr_.resize(natoms * 3);
+    dfcorr_.resize(static_cast<size_t>(natoms) * 3);
     dvcorr_.resize(9);
     VALUETYPE *dfcorr = &dfcorr_[0];
     VALUETYPE *dvcorr = &dvcorr_[0];
@@ -2071,7 +2071,7 @@ void select_map(std::vector<VT> &out,
       nall2++;
     }
   }
-  out.resize(nall2 * stride);
+  out.resize(static_cast<size_t>(nall2) * stride);
   DP_SelectMapInt(&in[0], &fwd_map[0], stride, nall1, nall2, &out[0]);
 };
 
diff --git a/source/api_c/tests/test_deepdipole_hpp.cc b/source/api_c/tests/test_deepdipole_hpp.cc
index 49958469e0..f781c34c5b 100644
--- a/source/api_c/tests/test_deepdipole_hpp.cc
+++ b/source/api_c/tests/test_deepdipole_hpp.cc
@@ -234,7 +234,7 @@ class TestInferDeepDipoleNew : public ::testing::Test {
       }
     }
 
-    expected_gv.resize(odim * 9);
+    expected_gv.resize(static_cast<size_t>(odim) * 9);
     for (int kk = 0; kk < odim; ++kk) {
       for (int ii = 0; ii < natoms; ++ii) {
         for (int dd = 0; dd < 9; ++dd) {
diff --git a/source/api_c/tests/test_deeppolar_hpp.cc b/source/api_c/tests/test_deeppolar_hpp.cc
index 1fc2075afb..63ebf5d760 100644
--- a/source/api_c/tests/test_deeppolar_hpp.cc
+++ b/source/api_c/tests/test_deeppolar_hpp.cc
@@ -466,7 +466,7 @@ class TestInferDeepPolarNew : public ::testing::Test {
       }
     }
 
-    expected_gv.resize(odim * 9);
+    expected_gv.resize(static_cast<size_t>(odim) * 9);
     for (int kk = 0; kk < odim; ++kk) {
       for (int ii = 0; ii < natoms; ++ii) {
         for (int dd = 0; dd < 9; ++dd) {
diff --git a/source/api_c/tests/test_deeppot_a_fparam_aparam_nframes.cc b/source/api_c/tests/test_deeppot_a_fparam_aparam_nframes.cc
index b94087916a..383c8f5fb1 100644
--- a/source/api_c/tests/test_deeppot_a_fparam_aparam_nframes.cc
+++ b/source/api_c/tests/test_deeppot_a_fparam_aparam_nframes.cc
@@ -126,7 +126,7 @@ class TestInferDeepPotAFparamAparamNFrames : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
@@ -767,7 +767,7 @@ class TestInferDeepPotAFparamAparamNFramesSingleParam : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
diff --git a/source/api_c/tests/test_deeppot_a_nframes_hpp.cc b/source/api_c/tests/test_deeppot_a_nframes_hpp.cc
index 1177957899..af132c0146 100644
--- a/source/api_c/tests/test_deeppot_a_nframes_hpp.cc
+++ b/source/api_c/tests/test_deeppot_a_nframes_hpp.cc
@@ -119,7 +119,7 @@ class TestInferDeepPotANFrames : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
@@ -728,7 +728,7 @@ class TestInferDeepPotANFramesNoPbc : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
diff --git a/source/api_c/tests/test_utils.h b/source/api_c/tests/test_utils.h
index 01636156b2..5167732bc8 100644
--- a/source/api_c/tests/test_utils.h
+++ b/source/api_c/tests/test_utils.h
@@ -42,7 +42,7 @@ inline void _fold_back(std::vector<VALUETYPE> &out,
                        const int nall,
                        const int ndim,
                        const int nframes = 1) {
-  out.resize(nframes * nloc * ndim);
+  out.resize(static_cast<size_t>(nframes) * nloc * ndim);
   _fold_back<VALUETYPE>(out.begin(), in.begin(), mapping, nloc, nall, ndim,
                         nframes);
 }
diff --git a/source/api_cc/src/DataModifier.cc b/source/api_cc/src/DataModifier.cc
index d687c02e75..c44bbceaa2 100644
--- a/source/api_cc/src/DataModifier.cc
+++ b/source/api_cc/src/DataModifier.cc
@@ -123,7 +123,7 @@ void DipoleChargeModifier::run_model(
   auto of = output_f.flat<MODELTYPE>();
   auto ov = output_v.flat<MODELTYPE>();
 
-  dforce.resize(nall * 3);
+  dforce.resize(static_cast<size_t>(nall) * 3);
   dvirial.resize(9);
   for (int ii = 0; ii < nall * 3; ++ii) {
     dforce[ii] = of(ii);
@@ -186,7 +186,7 @@ void DipoleChargeModifier::compute(
   int nall_real = real_bkw_map.size();
   int nloc_real = nall_real - nghost_real;
   if (nloc_real == 0) {
-    dfcorr_.resize(nall * 3);
+    dfcorr_.resize(static_cast<size_t>(nall) * 3);
     dvcorr_.resize(9);
     fill(dfcorr_.begin(), dfcorr_.end(), (VALUETYPE)0.0);
     fill(dvcorr_.begin(), dvcorr_.end(), (VALUETYPE)0.0);
@@ -196,8 +196,8 @@ void DipoleChargeModifier::compute(
   std::vector<VALUETYPE> dcoord_real;
   std::vector<VALUETYPE> delef_real;
   std::vector<int> datype_real;
-  dcoord_real.resize(nall_real * 3);
-  delef_real.resize(nall_real * 3);
+  dcoord_real.resize(static_cast<size_t>(nall_real) * 3);
+  delef_real.resize(static_cast<size_t>(nall_real) * 3);
   datype_real.resize(nall_real);
   // fwd map
   select_map<VALUETYPE>(dcoord_real, dcoord_, real_fwd_map, 3);
diff --git a/source/api_cc/src/DeepTensor.cc b/source/api_cc/src/DeepTensor.cc
index 655819e086..11a131a604 100644
--- a/source/api_cc/src/DeepTensor.cc
+++ b/source/api_cc/src/DeepTensor.cc
@@ -253,7 +253,7 @@ void DeepTensor::run_model(
   }
 
   // component-wise virial
-  dvirial_.resize(odim * 9);
+  dvirial_.resize(static_cast<size_t>(odim) * 9);
   for (unsigned ii = 0; ii < odim * 9; ++ii) {
     dvirial_[ii] = ov(ii);
   }
@@ -266,7 +266,7 @@ void DeepTensor::run_model(
   std::vector<int> sel_srt = sel_fwd;
   select_map<int>(sel_srt, sel_fwd, atommap.get_fwd_map(), 1);
   std::remove(sel_srt.begin(), sel_srt.end(), -1);
-  datom_tensor_.resize(nsel * odim);
+  datom_tensor_.resize(static_cast<size_t>(nsel) * odim);
   select_map<VALUETYPE>(datom_tensor_, datom_tensor, sel_srt, odim);
 
   // component-wise atomic virial
diff --git a/source/api_cc/src/common.cc b/source/api_cc/src/common.cc
index 33c433a90a..2f75aaa291 100644
--- a/source/api_cc/src/common.cc
+++ b/source/api_cc/src/common.cc
@@ -171,14 +171,15 @@ void deepmd::select_real_atoms_coord(std::vector<VALUETYPE>& dcoord,
   // resize to nall_real
   nall_real = bkw_map.size();
   nloc_real = nall_real - nghost_real;
-  dcoord.resize(nframes * nall_real * 3);
+  dcoord.resize(static_cast<size_t>(nframes) * nall_real * 3);
   datype.resize(nall_real);
   // fwd map
   select_map<VALUETYPE>(dcoord, dcoord_, fwd_map, 3, nframes, nall_real, nall);
   select_map<int>(datype, datype_, fwd_map, 1);
   // aparam
   if (daparam > 0) {
-    aparam.resize(nframes * (aparam_nall ? nall_real : nloc_real));
+    aparam.resize(static_cast<size_t>(nframes) *
+                  (aparam_nall ? nall_real : nloc_real));
     select_map<VALUETYPE>(aparam, aparam_, fwd_map, daparam, nframes,
                           (aparam_nall ? nall_real : nloc_real),
                           (aparam_nall ? nall : (nall - nghost)));
@@ -396,7 +397,7 @@ int deepmd::session_input_tensors(
 
   TensorShape coord_shape;
   coord_shape.AddDim(nframes);
-  coord_shape.AddDim(nall * 3);
+  coord_shape.AddDim(static_cast<int64_t>(nall) * 3);
   TensorShape type_shape;
   type_shape.AddDim(nframes);
   type_shape.AddDim(nall);
@@ -540,7 +541,7 @@ int deepmd::session_input_tensors(
 
   TensorShape coord_shape;
   coord_shape.AddDim(nframes);
-  coord_shape.AddDim(nall * 3);
+  coord_shape.AddDim(static_cast<int64_t>(nall) * 3);
   TensorShape type_shape;
   type_shape.AddDim(nframes);
   type_shape.AddDim(nall);
@@ -675,7 +676,7 @@ int deepmd::session_input_tensors_mixed_type(
 
   TensorShape coord_shape;
   coord_shape.AddDim(nframes);
-  coord_shape.AddDim(nall * 3);
+  coord_shape.AddDim(static_cast<int64_t>(nall) * 3);
   TensorShape type_shape;
   type_shape.AddDim(nframes);
   type_shape.AddDim(nall);
diff --git a/source/api_cc/tests/test_deepdipole.cc b/source/api_cc/tests/test_deepdipole.cc
index b8f2195728..86a8a4131f 100644
--- a/source/api_cc/tests/test_deepdipole.cc
+++ b/source/api_cc/tests/test_deepdipole.cc
@@ -238,7 +238,7 @@ class TestInferDeepDipoleNew : public ::testing::Test {
       }
     }
 
-    expected_gv.resize(odim * 9);
+    expected_gv.resize(static_cast<size_t>(odim) * 9);
     for (int kk = 0; kk < odim; ++kk) {
       for (int ii = 0; ii < natoms; ++ii) {
         for (int dd = 0; dd < 9; ++dd) {
diff --git a/source/api_cc/tests/test_deeppolar.cc b/source/api_cc/tests/test_deeppolar.cc
index d8ad497054..89014fd245 100644
--- a/source/api_cc/tests/test_deeppolar.cc
+++ b/source/api_cc/tests/test_deeppolar.cc
@@ -470,7 +470,7 @@ class TestInferDeepPolarNew : public ::testing::Test {
       }
     }
 
-    expected_gv.resize(odim * 9);
+    expected_gv.resize(static_cast<size_t>(odim) * 9);
     for (int kk = 0; kk < odim; ++kk) {
       for (int ii = 0; ii < natoms; ++ii) {
         for (int dd = 0; dd < 9; ++dd) {
diff --git a/source/api_cc/tests/test_deeppot_a_fparam_aparam_nframes.cc b/source/api_cc/tests/test_deeppot_a_fparam_aparam_nframes.cc
index 0f45eaabb0..0851523814 100644
--- a/source/api_cc/tests/test_deeppot_a_fparam_aparam_nframes.cc
+++ b/source/api_cc/tests/test_deeppot_a_fparam_aparam_nframes.cc
@@ -127,7 +127,7 @@ class TestInferDeepPotAFparamAparamNFrames : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
@@ -768,7 +768,7 @@ class TestInferDeepPotAFparamAparamNFramesSingleParam : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
diff --git a/source/api_cc/tests/test_deeppot_a_nframes.cc b/source/api_cc/tests/test_deeppot_a_nframes.cc
index 835971d106..c83a7a0b41 100644
--- a/source/api_cc/tests/test_deeppot_a_nframes.cc
+++ b/source/api_cc/tests/test_deeppot_a_nframes.cc
@@ -123,7 +123,7 @@ class TestInferDeepPotANFrames : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
@@ -732,7 +732,7 @@ class TestInferDeepPotANFramesNoPbc : public ::testing::Test {
     EXPECT_EQ(nframes * natoms * 3, expected_f.size());
     EXPECT_EQ(nframes * natoms * 9, expected_v.size());
     expected_tot_e.resize(nframes);
-    expected_tot_v.resize(nframes * 9);
+    expected_tot_v.resize(static_cast<size_t>(nframes) * 9);
     std::fill(expected_tot_e.begin(), expected_tot_e.end(), 0.);
     std::fill(expected_tot_v.begin(), expected_tot_v.end(), 0.);
     for (int kk = 0; kk < nframes; ++kk) {
diff --git a/source/api_cc/tests/test_utils.h b/source/api_cc/tests/test_utils.h
index 46732ca935..d06823b4e0 100644
--- a/source/api_cc/tests/test_utils.h
+++ b/source/api_cc/tests/test_utils.h
@@ -42,7 +42,7 @@ inline void _fold_back(std::vector<VALUETYPE> &out,
                        const int nall,
                        const int ndim,
                        const int nframes = 1) {
-  out.resize(nframes * nloc * ndim);
+  out.resize(static_cast<size_t>(nframes) * nloc * ndim);
   _fold_back<VALUETYPE>(out.begin(), in.begin(), mapping, nloc, nall, ndim,
                         nframes);
 }
diff --git a/source/ipi/driver.cc b/source/ipi/driver.cc
index 22d5415bd1..1e3d92eb5e 100644
--- a/source/ipi/driver.cc
+++ b/source/ipi/driver.cc
@@ -190,11 +190,11 @@ int main(int argc, char *argv[]) {
                     << std::endl;
         }
 
-        dcoord.resize(3 * natoms);
-        dforce.resize(3 * natoms, 0);
-        dcoord_tmp.resize(3 * natoms);
-        dforce_tmp.resize(3 * natoms, 0);
-        msg_buff = new double[3 * natoms];
+        dcoord.resize(3 * static_cast<size_t>(natoms));
+        dforce.resize(3 * static_cast<size_t>(natoms), 0);
+        dcoord_tmp.resize(3 * static_cast<size_t>(natoms));
+        dforce_tmp.resize(3 * static_cast<size_t>(natoms), 0);
+        msg_buff = new double[3 * static_cast<size_t>(natoms)];
       }
 
       // get coord
diff --git a/source/lib/src/ewald.cc b/source/lib/src/ewald.cc
index 0f3b960d9f..ec201c4d7d 100644
--- a/source/lib/src/ewald.cc
+++ b/source/lib/src/ewald.cc
@@ -98,7 +98,7 @@ void deepmd::ewald_recp(VALUETYPE& ener,
   // natoms
   int natoms = charge.size();
   // init returns
-  force.resize(natoms * 3);
+  force.resize(static_cast<size_t>(natoms) * 3);
   virial.resize(9);
   ener = 0;
   fill(force.begin(), force.end(), static_cast<VALUETYPE>(0));
@@ -179,7 +179,7 @@ void deepmd::ewald_recp(VALUETYPE& ener,
   std::vector<std::vector<VALUETYPE> > thread_force(nthreads);
   std::vector<std::vector<VALUETYPE> > thread_virial(nthreads);
   for (int ii = 0; ii < nthreads; ++ii) {
-    thread_force[ii].resize(natoms * 3, 0.);
+    thread_force[ii].resize(static_cast<size_t>(natoms) * 3, 0.);
     thread_virial[ii].resize(9, 0.);
   }
   // calculate ener, force and virial
diff --git a/source/lib/src/neighbor_list.cc b/source/lib/src/neighbor_list.cc
index fc797ce6a9..6723e3de66 100644
--- a/source/lib/src/neighbor_list.cc
+++ b/source/lib/src/neighbor_list.cc
@@ -784,7 +784,7 @@ void copy_coord(std::vector<double>& out_c,
   build_clist(clist, in_c, nloc, nat_stt, ncell, nat_stt, ncell, region, ncell);
 
   // copy local atoms
-  out_c.resize(nloc * 3);
+  out_c.resize(static_cast<size_t>(nloc) * 3);
   out_t.resize(nloc);
   mapping.resize(nloc);
   copy(in_c.begin(), in_c.end(), out_c.begin());
diff --git a/source/lib/src/pairwise.cc b/source/lib/src/pairwise.cc
index 3fea27bd71..f5b21d9856 100644
--- a/source/lib/src/pairwise.cc
+++ b/source/lib/src/pairwise.cc
@@ -93,7 +93,7 @@ void deepmd::dprc_pairwise_map_cpu(
   // (3, 4, 0, 1, 2, 10, 11),
   // (3, 4, 5, 6, 7, 10, -1),
   // (3, 4, 8, 9, -1, 10, -1)
-  forward_qmmm_map.resize((nfragments - 1) * map_size);
+  forward_qmmm_map.resize(static_cast<size_t>(nfragments - 1) * map_size);
   std::fill(forward_qmmm_map.begin(), forward_qmmm_map.end(), -1);
   int nqm_real = nloc;  // init for nfragments = 1
   for (int ii = 0; ii < nfragments - 1; ++ii) {
@@ -133,7 +133,7 @@ void deepmd::dprc_pairwise_map_cpu(
   // (2, 3, 4, 0, 1, -1, -1, -1, -1, -1, 5, 6)
   // (-1, -1, -1, 0, 1, 2, 3, 4, -1, -1, 5, -1)
   // (-1, -1, -1, 0, 1, -1, -1, -1, 2, 3, 5, -1)
-  backward_qmmm_map.resize((nfragments - 1) * nall);
+  backward_qmmm_map.resize(static_cast<size_t>(nfragments - 1) * nall);
   std::fill(backward_qmmm_map.begin(), backward_qmmm_map.end(), -1);
   for (int ii = 0; ii < nfragments - 1; ++ii) {
     for (int jj = 0; jj < map_size; ++jj) {
diff --git a/source/lib/src/prod_env_mat.cc b/source/lib/src/prod_env_mat.cc
index 63813069b0..81984c78e4 100644
--- a/source/lib/src/prod_env_mat.cc
+++ b/source/lib/src/prod_env_mat.cc
@@ -304,7 +304,8 @@ void deepmd::env_mat_nbor_update(InputNlist &inlist,
     max_nbor_size = _max_nbor_size;
 
     // copy nbor list from host to the device
-    std::vector<int> nbor_list_host(inum * max_nbor_size, 0);
+    std::vector<int> nbor_list_host(static_cast<size_t>(inum) * max_nbor_size,
+                                    0);
     int **_firstneigh = (int **)malloc(sizeof(int *) * inum);
     for (int ii = 0; ii < inum; ii++) {
       _firstneigh[ii] = nbor_list_dev + ii * max_nbor_size;
@@ -313,7 +314,7 @@ void deepmd::env_mat_nbor_update(InputNlist &inlist,
       }
     }
     memcpy_host_to_device(nbor_list_dev, &nbor_list_host[0],
-                          inum * max_nbor_size);
+                          static_cast<size_t>(inum) * max_nbor_size);
     memcpy_host_to_device(gpu_inlist.firstneigh, _firstneigh, inum);
     free(_firstneigh);
   }
diff --git a/source/lib/tests/test_coord.cc b/source/lib/tests/test_coord.cc
index c939dd6fa6..0427521416 100644
--- a/source/lib/tests/test_coord.cc
+++ b/source/lib/tests/test_coord.cc
@@ -234,7 +234,7 @@ TEST_F(TestCopyCoord, cpu) {
   // 	    << nloc << " "
   // 	    << nall << std::endl;
 
-  out_c.resize(nall * 3);
+  out_c.resize(static_cast<size_t>(nall) * 3);
   out_t.resize(nall);
   mapping.resize(nall);
 
@@ -322,7 +322,7 @@ TEST_F(TestCopyCoord, gpu) {
   deepmd::delete_device_memory(int_data_dev);
   EXPECT_EQ(ret, 0);
   EXPECT_EQ(nall, expected_nall);
-  out_c.resize(nall * 3);
+  out_c.resize(static_cast<size_t>(nall) * 3);
   out_t.resize(nall);
   mapping.resize(nall);
 
@@ -468,7 +468,7 @@ TEST_F(TestCopyCoordMoreCell, cpu) {
   // 	    << nloc << " "
   // 	    << nall << std::endl;
 
-  out_c.resize(nall * 3);
+  out_c.resize(static_cast<size_t>(nall) * 3);
   out_t.resize(nall);
   mapping.resize(nall);
 
@@ -556,7 +556,7 @@ TEST_F(TestCopyCoordMoreCell, gpu) {
   deepmd::delete_device_memory(int_data_dev);
   EXPECT_EQ(ret, 0);
   EXPECT_EQ(nall, expected_nall);
-  out_c.resize(nall * 3);
+  out_c.resize(static_cast<size_t>(nall) * 3);
   out_t.resize(nall);
   mapping.resize(nall);
 
diff --git a/source/lib/tests/test_map_aparam.cc b/source/lib/tests/test_map_aparam.cc
index 4adf3ffd98..061ae49f28 100644
--- a/source/lib/tests/test_map_aparam.cc
+++ b/source/lib/tests/test_map_aparam.cc
@@ -65,7 +65,7 @@ class TestMapAparam : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -74,7 +74,7 @@ class TestMapAparam : public ::testing::Test {
         nlist[ii * nnei + jj] = fmt_nlist_a[jj];
       }
     }
-    aparam.resize(nall * numb_aparam);
+    aparam.resize(static_cast<size_t>(nall) * numb_aparam);
     for (int ii = 0; ii < nall * numb_aparam; ++ii) {
       aparam[ii] = 10 - 0.1 * ii;
     }
diff --git a/source/lib/tests/test_pair_tab.cc b/source/lib/tests/test_pair_tab.cc
index 9f68cd98b9..7002beb1da 100644
--- a/source/lib/tests/test_pair_tab.cc
+++ b/source/lib/tests/test_pair_tab.cc
@@ -235,10 +235,10 @@ class TestPairTab : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
diff --git a/source/lib/tests/test_prod_force_a.cc b/source/lib/tests/test_prod_force_a.cc
index 2031f086b4..f49b173769 100644
--- a/source/lib/tests/test_prod_force_a.cc
+++ b/source/lib/tests/test_prod_force_a.cc
@@ -82,10 +82,10 @@ class TestProdForceA : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij_a.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij_a.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -105,7 +105,7 @@ class TestProdForceA : public ::testing::Test {
         }
       }
     }
-    net_deriv.resize(nloc * ndescrpt);
+    net_deriv.resize(static_cast<size_t>(nloc) * ndescrpt);
     for (int ii = 0; ii < nloc * ndescrpt; ++ii) {
       net_deriv[ii] = 10 - ii * 0.01;
     }
diff --git a/source/lib/tests/test_prod_force_grad_a.cc b/source/lib/tests/test_prod_force_grad_a.cc
index abb04eaa01..a946639638 100644
--- a/source/lib/tests/test_prod_force_grad_a.cc
+++ b/source/lib/tests/test_prod_force_grad_a.cc
@@ -93,10 +93,10 @@ class TestProdForceGradA : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij_a.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij_a.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -116,7 +116,7 @@ class TestProdForceGradA : public ::testing::Test {
         }
       }
     }
-    grad.resize(nloc * 3);
+    grad.resize(static_cast<size_t>(nloc) * 3);
     for (int ii = 0; ii < nloc * 3; ++ii) {
       grad[ii] = 10 - ii * 0.1;
     }
diff --git a/source/lib/tests/test_prod_force_grad_r.cc b/source/lib/tests/test_prod_force_grad_r.cc
index c8a27077c3..e143633bea 100644
--- a/source/lib/tests/test_prod_force_grad_r.cc
+++ b/source/lib/tests/test_prod_force_grad_r.cc
@@ -67,10 +67,10 @@ class TestProdForceGradR : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij_a.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij_a.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -90,7 +90,7 @@ class TestProdForceGradR : public ::testing::Test {
         }
       }
     }
-    grad.resize(nloc * 3);
+    grad.resize(static_cast<size_t>(nloc) * 3);
     for (int ii = 0; ii < nloc * 3; ++ii) {
       grad[ii] = 10 - ii * 0.1;
     }
diff --git a/source/lib/tests/test_prod_force_r.cc b/source/lib/tests/test_prod_force_r.cc
index ff3245742d..544152c759 100644
--- a/source/lib/tests/test_prod_force_r.cc
+++ b/source/lib/tests/test_prod_force_r.cc
@@ -79,10 +79,10 @@ class TestProdForceR : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij_a.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij_a.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -102,7 +102,7 @@ class TestProdForceR : public ::testing::Test {
         }
       }
     }
-    net_deriv.resize(nloc * ndescrpt);
+    net_deriv.resize(static_cast<size_t>(nloc) * ndescrpt);
     for (int ii = 0; ii < nloc * ndescrpt; ++ii) {
       net_deriv[ii] = 10 - ii * 0.01;
     }
diff --git a/source/lib/tests/test_prod_virial_a.cc b/source/lib/tests/test_prod_virial_a.cc
index b2f2a11989..c6fe254db8 100644
--- a/source/lib/tests/test_prod_virial_a.cc
+++ b/source/lib/tests/test_prod_virial_a.cc
@@ -118,10 +118,10 @@ class TestProdVirialA : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -144,7 +144,7 @@ class TestProdVirialA : public ::testing::Test {
         rij[ii * nnei * 3 + jj] = t_rij[jj];
       }
     }
-    net_deriv.resize(nloc * ndescrpt);
+    net_deriv.resize(static_cast<size_t>(nloc) * ndescrpt);
     for (int ii = 0; ii < nloc * ndescrpt; ++ii) {
       net_deriv[ii] = 10 - ii * 0.01;
     }
diff --git a/source/lib/tests/test_prod_virial_grad_a.cc b/source/lib/tests/test_prod_virial_grad_a.cc
index 09af51d6ed..598df91c86 100644
--- a/source/lib/tests/test_prod_virial_grad_a.cc
+++ b/source/lib/tests/test_prod_virial_grad_a.cc
@@ -87,10 +87,10 @@ class TestProdVirialGradA : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
diff --git a/source/lib/tests/test_prod_virial_grad_r.cc b/source/lib/tests/test_prod_virial_grad_r.cc
index 93a7291176..9b520ed898 100644
--- a/source/lib/tests/test_prod_virial_grad_r.cc
+++ b/source/lib/tests/test_prod_virial_grad_r.cc
@@ -61,10 +61,10 @@ class TestProdVirialGradR : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
diff --git a/source/lib/tests/test_prod_virial_r.cc b/source/lib/tests/test_prod_virial_r.cc
index aed4abc512..f0fab48e78 100644
--- a/source/lib/tests/test_prod_virial_r.cc
+++ b/source/lib/tests/test_prod_virial_r.cc
@@ -118,10 +118,10 @@ class TestProdVirialR : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    env.resize(nloc * ndescrpt);
-    env_deriv.resize(nloc * ndescrpt * 3);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    env.resize(static_cast<size_t>(nloc) * ndescrpt);
+    env_deriv.resize(static_cast<size_t>(nloc) * ndescrpt * 3);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -144,7 +144,7 @@ class TestProdVirialR : public ::testing::Test {
         rij[ii * nnei * 3 + jj] = t_rij[jj];
       }
     }
-    net_deriv.resize(nloc * ndescrpt);
+    net_deriv.resize(static_cast<size_t>(nloc) * ndescrpt);
     for (int ii = 0; ii < nloc * ndescrpt; ++ii) {
       net_deriv[ii] = 10 - ii * 0.01;
     }
diff --git a/source/lib/tests/test_soft_min_switch.cc b/source/lib/tests/test_soft_min_switch.cc
index f7a4f43b1a..fbce26e352 100644
--- a/source/lib/tests/test_soft_min_switch.cc
+++ b/source/lib/tests/test_soft_min_switch.cc
@@ -55,8 +55,8 @@ class TestSoftMinSwitch : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
diff --git a/source/lib/tests/test_soft_min_switch_force.cc b/source/lib/tests/test_soft_min_switch_force.cc
index dacc681792..a49661fdbd 100644
--- a/source/lib/tests/test_soft_min_switch_force.cc
+++ b/source/lib/tests/test_soft_min_switch_force.cc
@@ -76,8 +76,8 @@ class TestSoftMinSwitchForce : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -95,7 +95,7 @@ class TestSoftMinSwitchForce : public ::testing::Test {
       }
     }
     sw_value.resize(nloc);
-    sw_deriv.resize(nloc * nnei * 3);
+    sw_deriv.resize(static_cast<size_t>(nloc) * nnei * 3);
     deepmd::soft_min_switch_cpu<double>(&sw_value[0], &sw_deriv[0], &rij[0],
                                         &nlist[0], nloc, nnei, alpha, rmin,
                                         rmax);
diff --git a/source/lib/tests/test_soft_min_switch_force_grad.cc b/source/lib/tests/test_soft_min_switch_force_grad.cc
index 7c36296a79..9cef91bed0 100644
--- a/source/lib/tests/test_soft_min_switch_force_grad.cc
+++ b/source/lib/tests/test_soft_min_switch_force_grad.cc
@@ -56,8 +56,8 @@ class TestSoftMinSwitchForceGrad : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -75,11 +75,11 @@ class TestSoftMinSwitchForceGrad : public ::testing::Test {
       }
     }
     sw_value.resize(nloc);
-    sw_deriv.resize(nloc * nnei * 3);
+    sw_deriv.resize(static_cast<size_t>(nloc) * nnei * 3);
     deepmd::soft_min_switch_cpu<double>(&sw_value[0], &sw_deriv[0], &rij[0],
                                         &nlist[0], nloc, nnei, alpha, rmin,
                                         rmax);
-    grad.resize(nloc * 3);
+    grad.resize(static_cast<size_t>(nloc) * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       grad[ii] = 1.0 - ii * 0.1;
     }
diff --git a/source/lib/tests/test_soft_min_switch_virial.cc b/source/lib/tests/test_soft_min_switch_virial.cc
index 76ddf9fa7f..8b38805528 100644
--- a/source/lib/tests/test_soft_min_switch_virial.cc
+++ b/source/lib/tests/test_soft_min_switch_virial.cc
@@ -121,8 +121,8 @@ class TestSoftMinSwitchVirial : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -140,7 +140,7 @@ class TestSoftMinSwitchVirial : public ::testing::Test {
       }
     }
     sw_value.resize(nloc);
-    sw_deriv.resize(nloc * nnei * 3);
+    sw_deriv.resize(static_cast<size_t>(nloc) * nnei * 3);
     deepmd::soft_min_switch_cpu<double>(&sw_value[0], &sw_deriv[0], &rij[0],
                                         &nlist[0], nloc, nnei, alpha, rmin,
                                         rmax);
diff --git a/source/lib/tests/test_soft_min_switch_virial_grad.cc b/source/lib/tests/test_soft_min_switch_virial_grad.cc
index 315880b3ac..fef87d4d4e 100644
--- a/source/lib/tests/test_soft_min_switch_virial_grad.cc
+++ b/source/lib/tests/test_soft_min_switch_virial_grad.cc
@@ -56,8 +56,8 @@ class TestSoftMinSwitchVirialGrad : public ::testing::Test {
     }
     build_nlist(nlist_a_cpy, nlist_r_cpy, posi_cpy, nloc, rc, rc, nat_stt,
                 ncell, ext_stt, ext_end, region, ncell);
-    nlist.resize(nloc * nnei);
-    rij.resize(nloc * nnei * 3);
+    nlist.resize(static_cast<size_t>(nloc) * nnei);
+    rij.resize(static_cast<size_t>(nloc) * nnei * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       // format nlist and record
       format_nlist_i_cpu<double>(fmt_nlist_a, posi_cpy, atype_cpy, ii,
@@ -75,11 +75,11 @@ class TestSoftMinSwitchVirialGrad : public ::testing::Test {
       }
     }
     sw_value.resize(nloc);
-    sw_deriv.resize(nloc * nnei * 3);
+    sw_deriv.resize(static_cast<size_t>(nloc) * nnei * 3);
     deepmd::soft_min_switch_cpu<double>(&sw_value[0], &sw_deriv[0], &rij[0],
                                         &nlist[0], nloc, nnei, alpha, rmin,
                                         rmax);
-    grad.resize(nloc * 3);
+    grad.resize(static_cast<size_t>(nloc) * 3);
     for (int ii = 0; ii < nloc; ++ii) {
       grad[ii] = 1.0 - ii * 0.1;
     }
diff --git a/source/lmp/fix_dplr.cpp b/source/lmp/fix_dplr.cpp
index 628f435bb7..ea60023e26 100644
--- a/source/lmp/fix_dplr.cpp
+++ b/source/lmp/fix_dplr.cpp
@@ -517,7 +517,7 @@ void FixDPLR::pre_force(int vflag) {
 
   int odim = dpt.output_dim();
   assert(odim == 3);
-  dipole_recd.resize(nall * 3);
+  dipole_recd.resize(static_cast<size_t>(nall) * 3);
   fill(dipole_recd.begin(), dipole_recd.end(), 0.0);
   for (int ii = 0; ii < valid_pairs.size(); ++ii) {
     int idx0 = valid_pairs[ii].first;
diff --git a/source/lmp/pair_deepmd.cpp b/source/lmp/pair_deepmd.cpp
index 3a6c1c8bbf..90aa453143 100644
--- a/source/lmp/pair_deepmd.cpp
+++ b/source/lmp/pair_deepmd.cpp
@@ -204,7 +204,7 @@ static void make_uniform_aparam(vector<double> &daparam,
                                 const vector<double> &aparam,
                                 const int &nlocal) {
   unsigned dim_aparam = aparam.size();
-  daparam.resize(dim_aparam * nlocal);
+  daparam.resize(static_cast<size_t>(dim_aparam) * nlocal);
   for (int ii = 0; ii < nlocal; ++ii) {
     for (int jj = 0; jj < dim_aparam; ++jj) {
       daparam[ii * dim_aparam + jj] = aparam[jj];
@@ -247,7 +247,7 @@ void PairDeepMD::make_aparam_from_compute(vector<double> &aparam) {
 
   assert(compute);
   int nlocal = atom->nlocal;
-  aparam.resize(dim_aparam * nlocal);
+  aparam.resize(static_cast<size_t>(dim_aparam) * nlocal);
 
   if (!(compute->invoked_flag & Compute::INVOKED_PERATOM)) {
     compute->compute_peratom();
@@ -573,7 +573,7 @@ void PairDeepMD::compute(int eflag, int vflag) {
             error->one(FLERR, e.what());
           }
         } else {
-          dforce.resize((extend_inum + extend_nghost) * 3);
+          dforce.resize(static_cast<size_t>(extend_inum + extend_nghost) * 3);
           try {
             deep_pot.compute(dener, dforce, dvirial, extend_dcoord,
                              extend_dtype, dbox, extend_nghost, extend_lmp_list,
@@ -596,7 +596,7 @@ void PairDeepMD::compute(int eflag, int vflag) {
             error->one(FLERR, e.what());
           }
         } else {
-          dforce.resize((extend_inum + extend_nghost) * 3);
+          dforce.resize(static_cast<size_t>(extend_inum + extend_nghost) * 3);
           try {
             deep_pot.compute(dener, dforce, dvirial, extend_dcoord,
                              extend_dtype, dbox, extend_nghost, extend_lmp_list,
@@ -1495,7 +1495,7 @@ void PairDeepMD::extend(int &extend_inum,
   }
 
   // extend coord
-  extend_dcoord.resize(extend_nall * 3);
+  extend_dcoord.resize(static_cast<size_t>(extend_nall) * 3);
   for (int ii = 0; ii < nloc; ii++) {
     for (int jj = 0; jj < 3; jj++) {
       extend_dcoord[new_idx_map[ii] * 3 + jj] = dcoord[ii * 3 + jj];
diff --git a/source/lmp/pppm_dplr.cpp b/source/lmp/pppm_dplr.cpp
index faa80ee308..613a9f1c93 100644
--- a/source/lmp/pppm_dplr.cpp
+++ b/source/lmp/pppm_dplr.cpp
@@ -59,7 +59,7 @@ void PPPMDPLR::init() {
 
   int nlocal = atom->nlocal;
   // cout << " ninit pppm/dplr ---------------------- " << nlocal << endl;
-  fele.resize(nlocal * 3);
+  fele.resize(static_cast<size_t>(nlocal) * 3);
   fill(fele.begin(), fele.end(), 0.0);
 }
 
@@ -296,7 +296,7 @@ void PPPMDPLR::fieldforce_ik() {
   int nghost = atom->nghost;
   int nall = nlocal + nghost;
 
-  fele.resize(nlocal * 3);
+  fele.resize(static_cast<size_t>(nlocal) * 3);
   fill(fele.begin(), fele.end(), 0.0);
 
   for (i = 0; i < nlocal; i++) {
@@ -372,7 +372,7 @@ void PPPMDPLR::fieldforce_ad() {
   int nghost = atom->nghost;
   int nall = nlocal + nghost;
 
-  fele.resize(nlocal * 3);
+  fele.resize(static_cast<size_t>(nlocal) * 3);
   fill(fele.begin(), fele.end(), 0.0);
 
   for (i = 0; i < nlocal; i++) {
diff --git a/source/md/src/Convert.cc b/source/md/src/Convert.cc
index 198c746c23..b8014bf974 100644
--- a/source/md/src/Convert.cc
+++ b/source/md/src/Convert.cc
@@ -53,8 +53,8 @@ void Convert<VALUETYPE>::gro2nnp(vector<VALUETYPE>& coord,
   assert(posi.size() == idx_map_nnp2gro.size());
   assert(velo.size() == idx_map_nnp2gro.size());
   int natoms = idx_map_nnp2gro.size();
-  coord.resize(3 * natoms);
-  veloc.resize(3 * natoms);
+  coord.resize(3 * static_cast<size_t>(natoms));
+  veloc.resize(3 * static_cast<size_t>(natoms));
   for (unsigned ii = 0; ii < natoms; ++ii) {
     int gro_i = idx_map_nnp2gro[ii];
     for (int dd = 0; dd < 3; ++dd) {
diff --git a/source/md/src/Tabulated.cc b/source/md/src/Tabulated.cc
index 1ecf8ee53d..6e9777ea29 100644
--- a/source/md/src/Tabulated.cc
+++ b/source/md/src/Tabulated.cc
@@ -24,7 +24,7 @@ void Tabulated::reinit(const VALUETYPE rc,
   hi = 1. / hh;
   rc2 = rc * rc;
 
-  data.resize(tableLength * stride);
+  data.resize(static_cast<size_t>(tableLength) * stride);
 
   int ii;
   for (ii = 0; ii < tableLength - 1; ++ii) {
diff --git a/source/op/descrpt.cc b/source/op/descrpt.cc
index ef040c3de0..6362b8d37a 100644
--- a/source/op/descrpt.cc
+++ b/source/op/descrpt.cc
@@ -145,22 +145,22 @@ class DescrptOp : public OpKernel {
     // Create an output tensor
     TensorShape descrpt_shape;
     descrpt_shape.AddDim(nsamples);
-    descrpt_shape.AddDim(nloc * ndescrpt);
+    descrpt_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
     TensorShape descrpt_deriv_shape;
     descrpt_deriv_shape.AddDim(nsamples);
-    descrpt_deriv_shape.AddDim(nloc * ndescrpt * 12);
+    descrpt_deriv_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt * 12);
     TensorShape rij_shape;
     rij_shape.AddDim(nsamples);
-    rij_shape.AddDim(nloc * nnei * 3);
+    rij_shape.AddDim(static_cast<int64_t>(nloc) * nnei * 3);
     TensorShape nlist_shape;
     nlist_shape.AddDim(nsamples);
-    nlist_shape.AddDim(nloc * nnei);
+    nlist_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
     TensorShape axis_shape;
     axis_shape.AddDim(nsamples);
-    axis_shape.AddDim(nloc * 4);
+    axis_shape.AddDim(static_cast<int64_t>(nloc) * 4);
     TensorShape rot_mat_shape;
     rot_mat_shape.AddDim(nsamples);
-    rot_mat_shape.AddDim(nloc * 9);
+    rot_mat_shape.AddDim(static_cast<int64_t>(nloc) * 9);
 
     Tensor* descrpt_tensor = NULL;
     OP_REQUIRES_OK(context,
diff --git a/source/op/descrpt_se_a_ef.cc b/source/op/descrpt_se_a_ef.cc
index 030c184b46..96c953f167 100644
--- a/source/op/descrpt_se_a_ef.cc
+++ b/source/op/descrpt_se_a_ef.cc
@@ -161,16 +161,16 @@ class DescrptSeAEfOp : public OpKernel {
     // Create an output tensor
     TensorShape descrpt_shape;
     descrpt_shape.AddDim(nsamples);
-    descrpt_shape.AddDim(nloc * ndescrpt);
+    descrpt_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
     TensorShape descrpt_deriv_shape;
     descrpt_deriv_shape.AddDim(nsamples);
-    descrpt_deriv_shape.AddDim(nloc * ndescrpt * 3);
+    descrpt_deriv_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt * 3);
     TensorShape rij_shape;
     rij_shape.AddDim(nsamples);
-    rij_shape.AddDim(nloc * nnei * 3);
+    rij_shape.AddDim(static_cast<int64_t>(nloc) * nnei * 3);
     TensorShape nlist_shape;
     nlist_shape.AddDim(nsamples);
-    nlist_shape.AddDim(nloc * nnei);
+    nlist_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
 
     int context_output_index = 0;
     Tensor* descrpt_tensor = NULL;
diff --git a/source/op/descrpt_se_a_ef_para.cc b/source/op/descrpt_se_a_ef_para.cc
index 06f7f138fb..6dc4442ee6 100644
--- a/source/op/descrpt_se_a_ef_para.cc
+++ b/source/op/descrpt_se_a_ef_para.cc
@@ -161,16 +161,16 @@ class DescrptSeAEfParaOp : public OpKernel {
     // Create an output tensor
     TensorShape descrpt_shape;
     descrpt_shape.AddDim(nsamples);
-    descrpt_shape.AddDim(nloc * ndescrpt);
+    descrpt_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
     TensorShape descrpt_deriv_shape;
     descrpt_deriv_shape.AddDim(nsamples);
-    descrpt_deriv_shape.AddDim(nloc * ndescrpt * 3);
+    descrpt_deriv_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt * 3);
     TensorShape rij_shape;
     rij_shape.AddDim(nsamples);
-    rij_shape.AddDim(nloc * nnei * 3);
+    rij_shape.AddDim(static_cast<int64_t>(nloc) * nnei * 3);
     TensorShape nlist_shape;
     nlist_shape.AddDim(nsamples);
-    nlist_shape.AddDim(nloc * nnei);
+    nlist_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
 
     int context_output_index = 0;
     Tensor* descrpt_tensor = NULL;
diff --git a/source/op/descrpt_se_a_ef_vert.cc b/source/op/descrpt_se_a_ef_vert.cc
index d70e9b201b..9899e29f06 100644
--- a/source/op/descrpt_se_a_ef_vert.cc
+++ b/source/op/descrpt_se_a_ef_vert.cc
@@ -161,16 +161,16 @@ class DescrptSeAEfVertOp : public OpKernel {
     // Create an output tensor
     TensorShape descrpt_shape;
     descrpt_shape.AddDim(nsamples);
-    descrpt_shape.AddDim(nloc * ndescrpt);
+    descrpt_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
     TensorShape descrpt_deriv_shape;
     descrpt_deriv_shape.AddDim(nsamples);
-    descrpt_deriv_shape.AddDim(nloc * ndescrpt * 3);
+    descrpt_deriv_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt * 3);
     TensorShape rij_shape;
     rij_shape.AddDim(nsamples);
-    rij_shape.AddDim(nloc * nnei * 3);
+    rij_shape.AddDim(static_cast<int64_t>(nloc) * nnei * 3);
     TensorShape nlist_shape;
     nlist_shape.AddDim(nsamples);
-    nlist_shape.AddDim(nloc * nnei);
+    nlist_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
 
     int context_output_index = 0;
     Tensor* descrpt_tensor = NULL;
diff --git a/source/op/descrpt_se_a_mask.cc b/source/op/descrpt_se_a_mask.cc
index 4f133e5210..e27ea099ab 100644
--- a/source/op/descrpt_se_a_mask.cc
+++ b/source/op/descrpt_se_a_mask.cc
@@ -95,16 +95,18 @@ class DescrptSeAMaskOp : public OpKernel {
     // Create an output tensor
     TensorShape descrpt_shape;
     descrpt_shape.AddDim(nsamples);
-    descrpt_shape.AddDim(total_atom_num * total_atom_num * n_descrpt);
+    descrpt_shape.AddDim(static_cast<int64_t>(total_atom_num) * total_atom_num *
+                         n_descrpt);
     TensorShape descrpt_deriv_shape;
     descrpt_deriv_shape.AddDim(nsamples);
-    descrpt_deriv_shape.AddDim(total_atom_num * total_atom_num * n_descrpt * 3);
+    descrpt_deriv_shape.AddDim(static_cast<int64_t>(total_atom_num) *
+                               total_atom_num * n_descrpt * 3);
     TensorShape rij_shape;
     rij_shape.AddDim(nsamples);
-    rij_shape.AddDim(total_atom_num * total_atom_num * 3);
+    rij_shape.AddDim(static_cast<int64_t>(total_atom_num) * total_atom_num * 3);
     TensorShape nlist_shape;
     nlist_shape.AddDim(nsamples);
-    nlist_shape.AddDim(total_atom_num * total_atom_num);
+    nlist_shape.AddDim(static_cast<int64_t>(total_atom_num) * total_atom_num);
 
     int context_output_index = 0;
     Tensor *descrpt_tensor = NULL;
diff --git a/source/op/ewald_recp.cc b/source/op/ewald_recp.cc
index a0fbc7f580..72f3c3d5dc 100644
--- a/source/op/ewald_recp.cc
+++ b/source/op/ewald_recp.cc
@@ -70,7 +70,7 @@ class EwaldRecpOp : public OpKernel {
     energy_shape.AddDim(nsamples);
     TensorShape force_shape;
     force_shape.AddDim(nsamples);
-    force_shape.AddDim(nloc * 3);
+    force_shape.AddDim(static_cast<int64_t>(nloc) * 3);
     TensorShape virial_shape;
     virial_shape.AddDim(nsamples);
     virial_shape.AddDim(9);
diff --git a/source/op/map_aparam.cc b/source/op/map_aparam.cc
index d0ff08032d..7ac3b48a4f 100644
--- a/source/op/map_aparam.cc
+++ b/source/op/map_aparam.cc
@@ -61,7 +61,7 @@ class MapAparamOp : public OpKernel {
     // Create an output tensor
     TensorShape output_shape;
     output_shape.AddDim(nframes);
-    output_shape.AddDim(nloc * nnei * numb_aparam);
+    output_shape.AddDim(static_cast<int64_t>(nloc) * nnei * numb_aparam);
     Tensor* output_tensor = NULL;
     OP_REQUIRES_OK(context,
                    context->allocate_output(0, output_shape, &output_tensor));
diff --git a/source/op/neighbor_stat.cc b/source/op/neighbor_stat.cc
index d917c60a5f..d2a6b3ab31 100644
--- a/source/op/neighbor_stat.cc
+++ b/source/op/neighbor_stat.cc
@@ -112,7 +112,7 @@ class NeighborStatOp : public OpKernel {
       if (nei_mode == 1) {
         // Tensor FPTYPE_temp;
         TensorShape FPTYPE_shape;
-        FPTYPE_shape.AddDim(nall * 3);
+        FPTYPE_shape.AddDim(static_cast<int64_t>(nall) * 3);
         OP_REQUIRES_OK(context,
                        context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                               FPTYPE_shape, &tensor_list[0]));
@@ -125,20 +125,20 @@ class NeighborStatOp : public OpKernel {
                                               double_shape, &tensor_list[1]));
         // Tensor cpy_temp;
         TensorShape cpy_shape;
-        cpy_shape.AddDim(mem_cpy * 3);
+        cpy_shape.AddDim(static_cast<int64_t>(mem_cpy) * 3);
         OP_REQUIRES_OK(context,
                        context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                               cpy_shape, &tensor_list[3]));
         // Tensor t_temp;
         TensorShape t_shape;
-        t_shape.AddDim(mem_cpy * 2);
+        t_shape.AddDim(static_cast<int64_t>(mem_cpy) * 2);
         OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, t_shape,
                                                        &tensor_list[4]));
       }
 
       // Tensor nlist_temp;
       TensorShape nlist_shape;
-      nlist_shape.AddDim(nloc * 2);
+      nlist_shape.AddDim(static_cast<int64_t>(nloc) * 2);
       OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, nlist_shape,
                                                      &tensor_list[5]));
 
@@ -167,7 +167,7 @@ class NeighborStatOp : public OpKernel {
           rcut, max_cpy_trial, max_nnei_trial);
 
       TensorShape min_nbor_dist_shape;
-      min_nbor_dist_shape.AddDim(nloc * mem_nnei);
+      min_nbor_dist_shape.AddDim(static_cast<int64_t>(nloc) * mem_nnei);
       Tensor* min_nbor_dist_tensor = NULL;
       OP_REQUIRES_OK(context, context->allocate_output(context_output_index++,
                                                        min_nbor_dist_shape,
@@ -253,7 +253,7 @@ class NeighborStatOp : public OpKernel {
       }
       // allocate output tensor for deepmd-kit
       TensorShape min_nbor_dist_shape;
-      min_nbor_dist_shape.AddDim(nloc * MAX_NNEI);
+      min_nbor_dist_shape.AddDim(static_cast<int64_t>(nloc) * MAX_NNEI);
       Tensor* min_nbor_dist_tensor = NULL;
       OP_REQUIRES_OK(context, context->allocate_output(context_output_index++,
                                                        min_nbor_dist_shape,
diff --git a/source/op/pair_tab.cc b/source/op/pair_tab.cc
index e412aa6c2a..5c16e0faa4 100644
--- a/source/op/pair_tab.cc
+++ b/source/op/pair_tab.cc
@@ -103,10 +103,10 @@ class PairTabOp : public OpKernel {
     energy_shape.AddDim(nloc);
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     TensorShape virial_shape;
     virial_shape.AddDim(nframes);
-    virial_shape.AddDim(9 * nall);
+    virial_shape.AddDim(9 * static_cast<int64_t>(nall));
     Tensor* energy_tensor = NULL;
     Tensor* force_tensor = NULL;
     Tensor* virial_tensor = NULL;
diff --git a/source/op/prod_env_mat_multi_device.cc b/source/op/prod_env_mat_multi_device.cc
index 22654b5f3a..a99804cb9e 100644
--- a/source/op/prod_env_mat_multi_device.cc
+++ b/source/op/prod_env_mat_multi_device.cc
@@ -497,7 +497,7 @@ class ProdEnvMatAOp : public OpKernel {
         if (nei_mode == 1) {
           // Tensor FPTYPE_temp;
           TensorShape FPTYPE_shape;
-          FPTYPE_shape.AddDim(nall * 3);
+          FPTYPE_shape.AddDim(static_cast<int64_t>(nall) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 FPTYPE_shape, &tensor_list[0]));
@@ -510,20 +510,20 @@ class ProdEnvMatAOp : public OpKernel {
                                                 double_shape, &tensor_list[1]));
           // Tensor cpy_temp;
           TensorShape cpy_shape;
-          cpy_shape.AddDim(mem_cpy * 3);
+          cpy_shape.AddDim(static_cast<int64_t>(mem_cpy) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 cpy_shape, &tensor_list[3]));
           // Tensor t_temp;
           TensorShape t_shape;
-          t_shape.AddDim(mem_cpy * 2);
+          t_shape.AddDim(static_cast<int64_t>(mem_cpy) * 2);
           OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, t_shape,
                                                          &tensor_list[4]));
         }
 
         // Tensor nlist_temp;
         TensorShape nlist_shape;
-        nlist_shape.AddDim(nloc * 2);
+        nlist_shape.AddDim(static_cast<int64_t>(nloc) * 2);
         OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, nlist_shape,
                                                        &tensor_list[5]));
 
@@ -794,7 +794,7 @@ class ProdEnvMatROp : public OpKernel {
         if (nei_mode == 1) {
           // Tensor FPTYPE_temp;
           TensorShape FPTYPE_shape;
-          FPTYPE_shape.AddDim(nall * 3);
+          FPTYPE_shape.AddDim(static_cast<int64_t>(nall) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 FPTYPE_shape, &tensor_list[0]));
@@ -807,20 +807,20 @@ class ProdEnvMatROp : public OpKernel {
                                                 double_shape, &tensor_list[1]));
           // Tensor cpy_temp;
           TensorShape cpy_shape;
-          cpy_shape.AddDim(mem_cpy * 3);
+          cpy_shape.AddDim(static_cast<int64_t>(mem_cpy) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 cpy_shape, &tensor_list[3]));
           // Tensor t_temp;
           TensorShape t_shape;
-          t_shape.AddDim(mem_cpy * 2);
+          t_shape.AddDim(static_cast<int64_t>(mem_cpy) * 2);
           OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, t_shape,
                                                          &tensor_list[4]));
         }
 
         // Tensor nlist_temp;
         TensorShape nlist_shape;
-        nlist_shape.AddDim(nloc * 2);
+        nlist_shape.AddDim(static_cast<int64_t>(nloc) * 2);
         OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, nlist_shape,
                                                        &tensor_list[5]));
 
@@ -1066,10 +1066,10 @@ class ProdEnvMatAMixOp : public OpKernel {
     nlist_shape.AddDim(int_64(nloc) * nnei);
     TensorShape ntype_shape;
     ntype_shape.AddDim(nsamples);
-    ntype_shape.AddDim(nloc * nnei);
+    ntype_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
     TensorShape nmask_shape;
     nmask_shape.AddDim(nsamples);
-    nmask_shape.AddDim(nloc * nnei);
+    nmask_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
     // define output tensor
     int context_output_index = 0;
     Tensor* descrpt_tensor = NULL;
@@ -1137,7 +1137,7 @@ class ProdEnvMatAMixOp : public OpKernel {
         if (nei_mode == 1) {
           // Tensor FPTYPE_temp;
           TensorShape FPTYPE_shape;
-          FPTYPE_shape.AddDim(nall * 3);
+          FPTYPE_shape.AddDim(static_cast<int64_t>(nall) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 FPTYPE_shape, &tensor_list[0]));
@@ -1150,20 +1150,20 @@ class ProdEnvMatAMixOp : public OpKernel {
                                                 double_shape, &tensor_list[1]));
           // Tensor cpy_temp;
           TensorShape cpy_shape;
-          cpy_shape.AddDim(mem_cpy * 3);
+          cpy_shape.AddDim(static_cast<int64_t>(mem_cpy) * 3);
           OP_REQUIRES_OK(context,
                          context->allocate_temp(DataTypeToEnum<FPTYPE>::value,
                                                 cpy_shape, &tensor_list[3]));
           // Tensor t_temp;
           TensorShape t_shape;
-          t_shape.AddDim(mem_cpy * 2);
+          t_shape.AddDim(static_cast<int64_t>(mem_cpy) * 2);
           OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, t_shape,
                                                          &tensor_list[4]));
         }
 
         // Tensor nlist_temp;
         TensorShape nlist_shape;
-        nlist_shape.AddDim(nloc * 2);
+        nlist_shape.AddDim(static_cast<int64_t>(nloc) * 2);
         OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, nlist_shape,
                                                        &tensor_list[5]));
 
@@ -1296,7 +1296,7 @@ static int _norm_copy_coord_cpu(std::vector<FPTYPE>& coord_cpy,
   normalize_coord_cpu(&tmp_coord[0], nall, region);
   int tt;
   for (tt = 0; tt < max_cpy_trial; ++tt) {
-    coord_cpy.resize(mem_cpy * 3);
+    coord_cpy.resize(static_cast<size_t>(mem_cpy) * 3);
     type_cpy.resize(mem_cpy);
     idx_mapping.resize(mem_cpy);
     int ret =
@@ -1512,7 +1512,7 @@ static int _norm_copy_coord_gpu(OpKernelContext* context,
       mem_cpy *= 2;
       // Tensor cpy_temp;
       TensorShape cpy_shape;
-      cpy_shape.AddDim(mem_cpy * 3);
+      cpy_shape.AddDim(static_cast<int64_t>(mem_cpy) * 3);
       status = context->allocate_temp(DataTypeToEnum<FPTYPE>::value, cpy_shape,
                                       tensor_list + 3);
       if (!status.ok()) {
@@ -1520,7 +1520,7 @@ static int _norm_copy_coord_gpu(OpKernelContext* context,
       }
       // Tensor t_temp;
       TensorShape t_shape;
-      t_shape.AddDim(mem_cpy * 2);
+      t_shape.AddDim(static_cast<int64_t>(mem_cpy) * 2);
       status = context->allocate_temp(DT_INT32, t_shape, tensor_list + 4);
       if (!status.ok()) {
         return false;
diff --git a/source/op/prod_env_mat_multi_device_nvnmd.cc b/source/op/prod_env_mat_multi_device_nvnmd.cc
index 1cbfb968f1..d9f9275b86 100644
--- a/source/op/prod_env_mat_multi_device_nvnmd.cc
+++ b/source/op/prod_env_mat_multi_device_nvnmd.cc
@@ -156,7 +156,7 @@ static int _norm_copy_coord_cpu(std::vector<FPTYPE>& coord_cpy,
   normalize_coord_cpu(&tmp_coord[0], nall, region);
   int tt;
   for (tt = 0; tt < max_cpy_trial; ++tt) {
-    coord_cpy.resize(mem_cpy * 3);
+    coord_cpy.resize(static_cast<size_t>(mem_cpy) * 3);
     type_cpy.resize(mem_cpy);
     idx_mapping.resize(mem_cpy);
     int ret =
@@ -675,10 +675,10 @@ class ProdEnvMatAMixNvnmdQuantizeOp : public OpKernel {
     nlist_shape.AddDim(int_64(nloc) * nnei);
     TensorShape ntype_shape;
     ntype_shape.AddDim(nsamples);
-    ntype_shape.AddDim(nloc * nnei);
+    ntype_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
     TensorShape nmask_shape;
     nmask_shape.AddDim(nsamples);
-    nmask_shape.AddDim(nloc * nnei);
+    nmask_shape.AddDim(static_cast<int64_t>(nloc) * nnei);
     // define output tensor
     int context_output_index = 0;
     Tensor* descrpt_tensor = NULL;
@@ -707,7 +707,7 @@ class ProdEnvMatAMixNvnmdQuantizeOp : public OpKernel {
 
     Tensor fake_type_tensor;  // all zeros
     TensorShape fake_type_shape;
-    fake_type_shape.AddDim(nsamples * nall);
+    fake_type_shape.AddDim(static_cast<int64_t>(nsamples) * nall);
     OP_REQUIRES_OK(context, context->allocate_temp(DT_INT32, fake_type_shape,
                                                    &fake_type_tensor));
 
diff --git a/source/op/prod_force.cc b/source/op/prod_force.cc
index d8ced591b9..57d1cd1331 100644
--- a/source/op/prod_force.cc
+++ b/source/op/prod_force.cc
@@ -81,7 +81,7 @@ class ProdForceOp : public OpKernel {
     // Create an output tensor
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     // std::cout << "forcesahpe " << force_shape.dim_size(0) << " " <<
     // force_shape.dim_size(1) << std::endl;
     Tensor* force_tensor = NULL;
diff --git a/source/op/prod_force_grad.cc b/source/op/prod_force_grad.cc
index 2d14022279..c1cf63917e 100644
--- a/source/op/prod_force_grad.cc
+++ b/source/op/prod_force_grad.cc
@@ -92,7 +92,7 @@ class ProdForceGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/prod_force_multi_device.cc b/source/op/prod_force_multi_device.cc
index 3eaf005f9a..20cc96dd31 100644
--- a/source/op/prod_force_multi_device.cc
+++ b/source/op/prod_force_multi_device.cc
@@ -103,7 +103,7 @@ class ProdForceSeAOp : public OpKernel {
     // Create an output tensor
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     Tensor* force_tensor = NULL;
     int context_output_index = 0;
     OP_REQUIRES_OK(context,
@@ -200,7 +200,7 @@ class ProdForceSeROp : public OpKernel {
     // Create an output tensor
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     Tensor* force_tensor = NULL;
     int context_output_index = 0;
     OP_REQUIRES_OK(context,
diff --git a/source/op/prod_force_se_a_grad.cc b/source/op/prod_force_se_a_grad.cc
index 21dd4fe00a..5aaf030512 100644
--- a/source/op/prod_force_se_a_grad.cc
+++ b/source/op/prod_force_se_a_grad.cc
@@ -85,7 +85,7 @@ class ProdForceSeAGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/prod_force_se_a_mask.cc b/source/op/prod_force_se_a_mask.cc
index 32fcf54a79..aa4268434d 100644
--- a/source/op/prod_force_se_a_mask.cc
+++ b/source/op/prod_force_se_a_mask.cc
@@ -63,7 +63,7 @@ class ProdForceSeAMaskOp : public OpKernel {
     // Create an output tensor
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     // std::cout << "forcesahpe " << force_shape.dim_size(0) << " " <<
     // force_shape.dim_size(1) << std::endl;
     Tensor *force_tensor = NULL;
diff --git a/source/op/prod_force_se_a_mask_grad.cc b/source/op/prod_force_se_a_mask_grad.cc
index 6f841b1c7d..dabe405545 100644
--- a/source/op/prod_force_se_a_mask_grad.cc
+++ b/source/op/prod_force_se_a_mask_grad.cc
@@ -77,7 +77,7 @@ class ProdForceSeAMaskGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor *grad_net_tensor = NULL;
diff --git a/source/op/prod_force_se_r_grad.cc b/source/op/prod_force_se_r_grad.cc
index f0b4b18323..0b5338c241 100644
--- a/source/op/prod_force_se_r_grad.cc
+++ b/source/op/prod_force_se_r_grad.cc
@@ -77,7 +77,7 @@ class ProdForceSeRGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/prod_virial.cc b/source/op/prod_virial.cc
index 2719c6c670..10532d74db 100644
--- a/source/op/prod_virial.cc
+++ b/source/op/prod_virial.cc
@@ -96,7 +96,7 @@ class ProdVirialOp : public OpKernel {
                    context->allocate_output(0, virial_shape, &virial_tensor));
     TensorShape atom_virial_shape;
     atom_virial_shape.AddDim(nframes);
-    atom_virial_shape.AddDim(9 * nall);
+    atom_virial_shape.AddDim(9 * static_cast<int64_t>(nall));
     Tensor* atom_virial_tensor = NULL;
     OP_REQUIRES_OK(context, context->allocate_output(1, atom_virial_shape,
                                                      &atom_virial_tensor));
diff --git a/source/op/prod_virial_grad.cc b/source/op/prod_virial_grad.cc
index b06e273453..02feba4eee 100644
--- a/source/op/prod_virial_grad.cc
+++ b/source/op/prod_virial_grad.cc
@@ -101,7 +101,7 @@ class ProdVirialGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/prod_virial_multi_device.cc b/source/op/prod_virial_multi_device.cc
index 23b312b797..a544b010c5 100644
--- a/source/op/prod_virial_multi_device.cc
+++ b/source/op/prod_virial_multi_device.cc
@@ -93,7 +93,7 @@ class ProdVirialSeAOp : public OpKernel {
     virial_shape.AddDim(9);
     TensorShape atom_virial_shape;
     atom_virial_shape.AddDim(nframes);
-    atom_virial_shape.AddDim(9 * nall);
+    atom_virial_shape.AddDim(9 * static_cast<int64_t>(nall));
     int context_output_index = 0;
     Tensor* virial_tensor = NULL;
     OP_REQUIRES_OK(
@@ -192,7 +192,7 @@ class ProdVirialSeROp : public OpKernel {
     virial_shape.AddDim(9);
     TensorShape atom_virial_shape;
     atom_virial_shape.AddDim(nframes);
-    atom_virial_shape.AddDim(9 * nall);
+    atom_virial_shape.AddDim(9 * static_cast<int64_t>(nall));
     int context_output_index = 0;
     Tensor* virial_tensor = NULL;
     OP_REQUIRES_OK(
diff --git a/source/op/prod_virial_se_a_grad.cc b/source/op/prod_virial_se_a_grad.cc
index a22401d654..d6c55b6969 100644
--- a/source/op/prod_virial_se_a_grad.cc
+++ b/source/op/prod_virial_se_a_grad.cc
@@ -94,7 +94,7 @@ class ProdVirialSeAGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/prod_virial_se_r_grad.cc b/source/op/prod_virial_se_r_grad.cc
index b874c828df..40c2828ca7 100644
--- a/source/op/prod_virial_se_r_grad.cc
+++ b/source/op/prod_virial_se_r_grad.cc
@@ -86,7 +86,7 @@ class ProdVirialSeRGradOp : public OpKernel {
     // Create an output tensor
     TensorShape grad_net_shape;
     grad_net_shape.AddDim(nframes);
-    grad_net_shape.AddDim(nloc * ndescrpt);
+    grad_net_shape.AddDim(static_cast<int64_t>(nloc) * ndescrpt);
 
     // allocate the output tensor
     Tensor* grad_net_tensor = NULL;
diff --git a/source/op/soft_min.cc b/source/op/soft_min.cc
index 4062ddc4cb..85aade5e7b 100644
--- a/source/op/soft_min.cc
+++ b/source/op/soft_min.cc
@@ -94,7 +94,7 @@ class SoftMinSwitchOp : public OpKernel {
     sw_value_shape.AddDim(nloc);
     TensorShape sw_deriv_shape;
     sw_deriv_shape.AddDim(nframes);
-    sw_deriv_shape.AddDim(3 * nnei * nloc);
+    sw_deriv_shape.AddDim(3 * static_cast<int64_t>(nnei) * nloc);
     Tensor* sw_value_tensor = NULL;
     Tensor* sw_deriv_tensor = NULL;
     tmp_idx = 0;
diff --git a/source/op/soft_min_force.cc b/source/op/soft_min_force.cc
index a2970f4c3a..0801170597 100644
--- a/source/op/soft_min_force.cc
+++ b/source/op/soft_min_force.cc
@@ -73,7 +73,7 @@ class SoftMinForceOp : public OpKernel {
     // Create an output tensor
     TensorShape force_shape;
     force_shape.AddDim(nframes);
-    force_shape.AddDim(3 * nall);
+    force_shape.AddDim(3 * static_cast<int64_t>(nall));
     Tensor* force_tensor = NULL;
     OP_REQUIRES_OK(context,
                    context->allocate_output(0, force_shape, &force_tensor));
diff --git a/source/op/soft_min_virial.cc b/source/op/soft_min_virial.cc
index 91a94e01c3..26daa78604 100644
--- a/source/op/soft_min_virial.cc
+++ b/source/op/soft_min_virial.cc
@@ -89,7 +89,7 @@ class SoftMinVirialOp : public OpKernel {
                    context->allocate_output(0, virial_shape, &virial_tensor));
     TensorShape atom_virial_shape;
     atom_virial_shape.AddDim(nframes);
-    atom_virial_shape.AddDim(9 * nall);
+    atom_virial_shape.AddDim(9 * static_cast<int64_t>(nall));
     Tensor* atom_virial_tensor = NULL;
     OP_REQUIRES_OK(context, context->allocate_output(1, atom_virial_shape,
                                                      &atom_virial_tensor));