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(pypolymlp-interface)= | ||
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# Force constants calculation using pypolymlp (machine learning potential) | ||
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**This is an experimental feature.** | ||
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With the `--pypolymlp` option, phono3py can interface with the polynomial | ||
machine learning potential (MLP) code, | ||
[pypolymlp](https://github.com/sekocha/pypolymlp), to perform training and | ||
evaluation tasks of MLPs. This feature aims to reduce the computational cost of | ||
anharmonic force constant calculations by using MLPs as an intermediary layer, | ||
efficiently representing atomic interactions. | ||
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The training process involves using a dataset consisting of supercell | ||
displacements, forces, and energies. The trained MLPs are then employed to | ||
compute forces for supercells with specific displacements. | ||
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For more details on the methodology, refer to <u>A. Togo and A. Seko, J. Chem. Phys. | ||
**160**, 211001 (2024)</u> [[doi](https://doi.org/10.1063/5.0211296)]. | ||
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An example of its usage can be found in the `example/NaCl-pypolymlp` directory | ||
in the distribution from GitHub or PyPI. | ||
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## Requirement | ||
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- [pypolymlp](https://github.com/sekocha/pypolymlp) | ||
- [symfc](https://github.com/symfc/symfc) | ||
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## Workflow | ||
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1. Generate random displacements in supercells. Use {ref}`--rd | ||
<random_displacements_option>` option. | ||
2. Calculate corresponding forces and energies in supercells. Use of VASP | ||
interface is recommended for {ref}`--sp <sp_option>` option is supported. | ||
3. Prepare dataset composed of displacements, forces, and energies in | ||
supercells. The dataset must be stored in a phono3py-yaml-like file, e.g., | ||
`phono3py_params.yaml`. Use {ref}`--cf3 <cf3_option>` and {ref}`--sp | ||
<sp_option>` option simultaneously. | ||
4. Develop MLPs. At this step `phono3py.pmlp` is saved. | ||
5. Generate displacements in supercells either systematic or random displacements. | ||
6. Evaluate MLPs for forces of the supercells generated in step 5. | ||
7. Calculate force constants from displacement-force dataset from steps 5 and 6. | ||
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The steps 4-7 are executed in running phono3py with `--pypolymlp` | ||
option. | ||
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### Steps 1-3: Dataset preparation | ||
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For the training, the following supercell data are required in the phono3py | ||
setting to use pypolymlp: | ||
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- Displacements | ||
- Forces | ||
- Total energies | ||
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These data must be stored in phono3py.yaml-like file. | ||
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The supercells with displacements are generated by | ||
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``` | ||
% phono3py --pa auto --rd 100 -c POSCAR-unitcell --dim 2 2 2 | ||
_ _____ | ||
_ __ | |__ ___ _ __ ___|___ / _ __ _ _ | ||
| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | | | ||
| |_) | | | | (_) | | | | (_) |__) | |_) | |_| | | ||
| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, | | ||
|_| |_| |___/ | ||
3.5.0 | ||
-------------------------[time 2024-09-19 14:40:00]------------------------- | ||
Compiled with OpenMP support (max 10 threads). | ||
Python version 3.12.4 | ||
Spglib version 2.5.0 | ||
Unit cell was read from "POSCAR-unitcell". | ||
-------------------------------- unit cell --------------------------------- | ||
Lattice vectors: | ||
a 5.603287477054753 0.000000000000000 0.000000000000000 | ||
b 0.000000000000000 5.603287477054753 0.000000000000000 | ||
c 0.000000000000000 0.000000000000000 5.603287477054753 | ||
Atomic positions (fractional): | ||
1 Na 0.00000000000000 0.00000000000000 0.00000000000000 22.990 | ||
2 Na 0.00000000000000 0.50000000000000 0.50000000000000 22.990 | ||
3 Na 0.50000000000000 0.00000000000000 0.50000000000000 22.990 | ||
4 Na 0.50000000000000 0.50000000000000 0.00000000000000 22.990 | ||
5 Cl 0.50000000000000 0.50000000000000 0.50000000000000 35.453 | ||
6 Cl 0.50000000000000 0.00000000000000 0.00000000000000 35.453 | ||
7 Cl 0.00000000000000 0.50000000000000 0.00000000000000 35.453 | ||
8 Cl 0.00000000000000 0.00000000000000 0.50000000000000 35.453 | ||
---------------------------------------------------------------------------- | ||
Supercell (dim): [2 2 2] | ||
Primitive matrix: | ||
[0. 0.5 0.5] | ||
[0.5 0. 0.5] | ||
[0.5 0.5 0. ] | ||
Displacement distance: 0.03 | ||
Number of displacements: 100 | ||
NAC parameters were read from "BORN". | ||
Spacegroup: Fm-3m (225) | ||
Displacement dataset was written in "phono3py_disp.yaml". | ||
-------------------------[time 2024-09-19 14:40:00]------------------------- | ||
_ | ||
___ _ __ __| | | ||
/ _ \ '_ \ / _` | | ||
| __/ | | | (_| | | ||
\___|_| |_|\__,_| | ||
``` | ||
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For the generated supercells, forces and energies are calculated. Here it is | ||
assumed to use the VASP code. Once the calculations are complete, the data | ||
(forces and energies) can be extracted using the following command: | ||
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```bash | ||
% phono3py --sp --cf3 vasprun_xmls/vasprun-{00001..00100}.xml | ||
``` | ||
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This command extracts the necessary data and stores it in the | ||
`phono3py_params.yaml` file. For more details, refer to the description of the | ||
{ref}`--sp <sp_option>` option. Currently, supercell energy extraction from | ||
calculator outputs is only supported when using the VASP interface. | ||
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``````{note} | ||
A set of the VASP calculation results is placed in `example/NaCl-rd`. It is | ||
obtained by | ||
```bash | ||
% tar xvfa ../NaCl-rd/vasprun_xmls.tar.xz | ||
``` | ||
`````` | ||
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### Steps 4-7: Force constants calculation (systematic displacements in step 5) | ||
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After developing MLPs, displacements are generated systematically considering | ||
crystal symmetry. | ||
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Having `phono3py_params.yaml`, phono3py is executed with `--pypolymlp` option, | ||
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``` | ||
% phono3py-load --pypolymlp phono3py_params.yaml | ||
_ _____ | ||
_ __ | |__ ___ _ __ ___|___ / _ __ _ _ | ||
| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | | | ||
| |_) | | | | (_) | | | | (_) |__) | |_) | |_| | | ||
| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, | | ||
|_| |_| |___/ | ||
3.5.0 | ||
-------------------------[time 2024-09-19 15:20:27]------------------------- | ||
Compiled with OpenMP support (max 10 threads). | ||
Running in phono3py.load mode. | ||
Python version 3.12.6 | ||
Spglib version 2.5.0 | ||
----------------------------- General settings ----------------------------- | ||
HDF5 data compression filter: gzip | ||
Crystal structure was read from "phono3py_params.yaml". | ||
Supercell (dim): [2 2 2] | ||
Primitive matrix: | ||
[0. 0.5 0.5] | ||
[0.5 0. 0.5] | ||
[0.5 0.5 0. ] | ||
Spacegroup: Fm-3m (225) | ||
Use -v option to watch primitive cell, unit cell, and supercell structures. | ||
NAC parameters were read from "phono3py_params.yaml". | ||
----------------------------- Force constants ------------------------------ | ||
Displacement dataset for fc3 was read from "phono3py_params.yaml". | ||
----------------------------- pypolymlp start ------------------------------ | ||
Pypolymlp is a generator of polynomial machine learning potentials. | ||
Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023). | ||
Pypolymlp is developed at https://github.com/sekocha/pypolymlp. | ||
Developing MLPs by pypolymlp... | ||
Regression: cholesky decomposition ... | ||
- alpha: 0.001 | ||
- alpha: 0.01 | ||
- alpha: 0.1 | ||
- alpha: 1.0 | ||
- alpha: 10.0 | ||
Clear training X.T @ X | ||
Calculate X.T @ X for test data | ||
Clear test X.T @ X | ||
Regression: model selection ... | ||
- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14 | ||
- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14 | ||
- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961 | ||
- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742 | ||
- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584 | ||
MLPs were written into "phono3py.pmlp" | ||
------------------------------ pypolymlp end ------------------------------- | ||
Generate displacements | ||
Displacement distance: 0.001 | ||
Evaluate forces in 292 supercells by pypolymlp | ||
Computing fc3[ 1, x, x ] using numpy.linalg.pinv. | ||
Displacements (in Angstrom): | ||
[ 0.0010 0.0000 0.0000] | ||
[-0.0010 0.0000 0.0000] | ||
Computing fc3[ 33, x, x ] using numpy.linalg.pinv. | ||
Displacements (in Angstrom): | ||
[ 0.0010 0.0000 0.0000] | ||
[-0.0010 0.0000 0.0000] | ||
Expanding fc3. | ||
fc3 was symmetrized. | ||
fc2 was symmetrized. | ||
Max drift of fc3: -0.000000 (zzz) -0.000000 (zzz) -0.000000 (zzz) | ||
Max drift of fc2: -0.000000 (zz) -0.000000 (zz) | ||
fc3 was written into "fc3.hdf5". | ||
fc2 was written into "fc2.hdf5". | ||
----------- None of ph-ph interaction calculation was performed. ----------- | ||
Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml". | ||
Summary of calculation was written in "phono3py.yaml". | ||
-------------------------[time 2024-09-19 15:21:41]------------------------- | ||
_ | ||
___ _ __ __| | | ||
/ _ \ '_ \ / _` | | ||
| __/ | | | (_| | | ||
\___|_| |_|\__,_| | ||
``` | ||
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Information about the development of MLPs using pypolymlp is provided between | ||
the `pypolymlp start` and `pypolymlp end` sections. The polynomial MLPs are | ||
saved in the `phono3py.pmlp` file, which can be reused in subsequent phono3py | ||
executions with the `--pypolymlp` option when only displacements (and no forces) | ||
are provided. | ||
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After the MLPs are developed, systematic displacements, such as those involving | ||
the displacement of one or two atoms in supercells, are generated with a | ||
displacement distance of 0.001 Angstrom. The forces for these supercells are | ||
then evaluated using pypolymlp. Both the generated displacements and the | ||
corresponding forces are stored in the `phono3py_mlp_eval_dataset` file. | ||
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### Steps 4-6: Force constants calculation (random displacements in step 5) | ||
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After developing MLPs, random displacements are generated by specifying | ||
{ref}`--rd <random_displacements_option>` option. To compute force constants | ||
with random displacements, an external force constants calculator is necessary. | ||
For this, symfc is used which is invoked by `--symfc` option. | ||
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Having `phono3py_params.yaml`, phono3py is executed with `--pypolymlp` option, | ||
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``` | ||
% phono3py-load --pypolymlp --rd 200 --symfc phono3py_params.yaml | ||
_ _____ | ||
_ __ | |__ ___ _ __ ___|___ / _ __ _ _ | ||
| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | | | ||
| |_) | | | | (_) | | | | (_) |__) | |_) | |_| | | ||
| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, | | ||
|_| |_| |___/ | ||
3.5.0-dev22+g575c4107 | ||
-------------------------[time 2024-09-19 15:33:23]------------------------- | ||
Compiled with OpenMP support (max 10 threads). | ||
Running in phono3py.load mode. | ||
Python version 3.12.6 | ||
Spglib version 2.5.0 | ||
----------------------------- General settings ----------------------------- | ||
HDF5 data compression filter: gzip | ||
Crystal structure was read from "phono3py_params.yaml". | ||
Supercell (dim): [2 2 2] | ||
Primitive matrix: | ||
[0. 0.5 0.5] | ||
[0.5 0. 0.5] | ||
[0.5 0.5 0. ] | ||
Spacegroup: Fm-3m (225) | ||
Use -v option to watch primitive cell, unit cell, and supercell structures. | ||
NAC parameters were read from "phono3py_params.yaml". | ||
----------------------------- Force constants ------------------------------ | ||
Displacement dataset for fc3 was read from "phono3py_params.yaml". | ||
----------------------------- pypolymlp start ------------------------------ | ||
Pypolymlp is a generator of polynomial machine learning potentials. | ||
Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023). | ||
Pypolymlp is developed at https://github.com/sekocha/pypolymlp. | ||
Developing MLPs by pypolymlp... | ||
Regression: cholesky decomposition ... | ||
- alpha: 0.001 | ||
- alpha: 0.01 | ||
- alpha: 0.1 | ||
- alpha: 1.0 | ||
- alpha: 10.0 | ||
Clear training X.T @ X | ||
Calculate X.T @ X for test data | ||
Clear test X.T @ X | ||
Regression: model selection ... | ||
- alpha = 1.000e-03 : rmse (train, test) = 9.39542e+14 9.39543e+14 | ||
- alpha = 1.000e-02 : rmse (train, test) = 9.39542e+14 9.39543e+14 | ||
- alpha = 1.000e-01 : rmse (train, test) = 0.03738 0.04961 | ||
- alpha = 1.000e+00 : rmse (train, test) = 0.03900 0.04742 | ||
- alpha = 1.000e+01 : rmse (train, test) = 0.04058 0.04584 | ||
MLPs were written into "phono3py.pmlp" | ||
------------------------------ pypolymlp end ------------------------------- | ||
Generate random displacements | ||
Twice of number of snapshots will be generated for plus-minus displacements. | ||
Displacement distance: 0.001 | ||
Evaluate forces in 400 supercells by pypolymlp | ||
-------------------------------- Symfc start ------------------------------- | ||
Symfc is a non-trivial force constants calculator. Please cite the paper: | ||
A. Seko and A. Togo, arXiv:2403.03588. | ||
Symfc is developed at https://github.com/symfc/symfc. | ||
Computing [2, 3] order force constants. | ||
Increase log-level to watch detailed symfc log. | ||
--------------------------------- Symfc end -------------------------------- | ||
-------------------------------- Symfc start ------------------------------- | ||
Symfc is a non-trivial force constants calculator. Please cite the paper: | ||
A. Seko and A. Togo, arXiv:2403.03588. | ||
Symfc is developed at https://github.com/symfc/symfc. | ||
Computing [2] order force constants. | ||
Increase log-level to watch detailed symfc log. | ||
--------------------------------- Symfc end -------------------------------- | ||
Max drift of fc3: -0.000000 (xyx) 0.000000 (zyy) -0.000000 (xyx) | ||
Max drift of fc2: 0.000000 (xx) 0.000000 (xx) | ||
fc3 was written into "fc3.hdf5". | ||
fc2 was written into "fc2.hdf5". | ||
----------- None of ph-ph interaction calculation was performed. ----------- | ||
Dataset generated using MMLPs was written in "phono3py_mlp_eval_dataset.yaml". | ||
Summary of calculation was written in "phono3py.yaml". | ||
-------------------------[time 2024-09-19 15:34:41]------------------------- | ||
_ | ||
___ _ __ __| | | ||
/ _ \ '_ \ / _` | | ||
| __/ | | | (_| | | ||
\___|_| |_|\__,_| | ||
``` | ||
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The development of MLPs follows the same procedure as described for the | ||
systematic displacements (in step 5) above. | ||
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After the MLPs are developed, 200 supercells with random directional | ||
displacements are generated. These displacements are then inverted, resulting in | ||
an additional 200 supercells. In total, 400 supercells are created. The forces | ||
for these supercells are then evaluated. Finally, the force constants are | ||
calculated using symfc. |
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# epsilon and Z* of atoms 1 2 | ||
2.56345522 0.00000000 -0.00000000 0.00000000 2.56345522 -0.00000000 0.00000000 -0.00000000 2.56345522 | ||
1.09044426 0.00000000 -0.00000000 0.00000000 1.09044426 -0.00000000 0.00000000 -0.00000000 1.09044426 | ||
-1.09044426 -0.00000000 0.00000000 -0.00000000 -1.09044426 0.00000000 -0.00000000 0.00000000 -1.09044426 |
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generated by phonopy | ||
1.0 | ||
5.6032874770547529 0.0000000000000000 0.0000000000000000 | ||
0.0000000000000000 5.6032874770547529 0.0000000000000000 | ||
0.0000000000000000 0.0000000000000000 5.6032874770547529 | ||
Na Cl | ||
4 4 | ||
Direct | ||
0.0000000000000000 0.0000000000000000 0.0000000000000000 | ||
0.0000000000000000 0.5000000000000000 0.5000000000000000 | ||
0.5000000000000000 0.0000000000000000 0.5000000000000000 | ||
0.5000000000000000 0.5000000000000000 0.0000000000000000 | ||
0.5000000000000000 0.5000000000000000 0.5000000000000000 | ||
0.5000000000000000 0.0000000000000000 0.0000000000000000 | ||
0.0000000000000000 0.5000000000000000 0.0000000000000000 | ||
0.0000000000000000 0.0000000000000000 0.5000000000000000 |
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