main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# Approximation and inference of non-Markov models of gene expression by neural network chemical master equations\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Flux, DiffEqSensitivity, DifferentialEquations\n",
    "using Distributions, Distances\n",
    "using DelimitedFiles, Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "Random.seed!(1234);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load train data\n",
    "source_data = readdlm(\"$(homedir())/Desktop/NN-CME/SSA_sinlge_channel_tau10.csv\",',');\n",
    "\n",
    "# truncation\n",
    "N = Int(maximum(source_data));\n",
    "\n",
    "# randomly select samples\n",
    "trajectory = 1000;\n",
    "train_data = source_data[:, rand(2:50001, trajectory)];\n",
    "(nrows, ncols) = size(train_data);\n",
    "\n",
    "# calculate the probabilities at 0~N\n",
    "train_sol = zeros(N+1, 51);\n",
    "for i in 0:N\n",
    "        for j in 1:51\n",
    "                count = 0;\n",
    "                for k in 1:trajectory\n",
    "                         if train_data[j,k] == i\n",
    "                                  count = count + 1/trajectory;\n",
    "                         end\n",
    "                end\n",
    "                train_sol[i+1, j] = count;\n",
    "        end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train neural network chemical master equation (NN-CME) for Model I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "128.007303 seconds (982.19 M allocations: 152.868 GiB, 6.34% gc time)\n",
      "141.436129 seconds (1.11 G allocations: 174.257 GiB, 6.32% gc time)\n",
      " 34.916876 seconds (277.44 M allocations: 43.530 GiB, 5.38% gc time)\n"
     ]
    }
   ],
   "source": [
    "# model initialization\n",
    "model = Chain(Dense(N+1, 100, tanh), Dense(100, N), x -> x .+ [i/10 for i in 1:N], x -> relu.(x));\n",
    "p1, re = Flux.destructure(model);\n",
    "ps = Flux.params(p1);\n",
    "\n",
    "# define the CME\n",
    "function CME(du, u, p, t)\n",
    "     ρ = 20.0;  \n",
    "     NN = re(p)(u);\n",
    "    \n",
    "     du[1] = -ρ*u[1] + NN[1]*u[2];\n",
    "     for i in 2:N\n",
    "           du[i] = ρ*u[i-1] + (-ρ - NN[i-1])*u[i] + NN[i]*u[i+1];\n",
    "     end\n",
    "     du[N+1] = ρ*u[N] + (-ρ - NN[N])*u[N+1];\n",
    "end\n",
    "\n",
    "# initialize the ODE solver\n",
    "u0 = [1.; zeros(N)]; \n",
    "tspan = (0.0, 50.0);\n",
    "problem = ODEProblem(CME, u0, tspan, p1);\n",
    "\n",
    "# define the objective function\n",
    "function loss_adjoint()\n",
    "      # solve ODE problem and save at the selected time\n",
    "      sol = Array(solve(problem, Tsit5(), u0=u0, p=p1, saveat=[4,8,14,20,26,32,38,44,50]));\n",
    "      # calculate MSE at the selected time between train data and fitted data\n",
    "      Flux.mse(sol, train_sol[:, [3,5,8,11,14,17,20,23,26]])\n",
    "\n",
    "end\n",
    "\n",
    "# start training with piece-wise learning rate\n",
    "@time Flux.train!(loss_adjoint, ps, Iterators.repeated((), 7), ADAM(0.25))\n",
    "@time Flux.train!(loss_adjoint, ps, Iterators.repeated((), 8), ADAM(0.12))\n",
    "@time Flux.train!(loss_adjoint, ps, Iterators.repeated((), 2), ADAM(0.02))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate after training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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       "  1558.77,1486.45 1561.88,1486.45 1565,1486.45 1568.11,1486.45 1571.23,1486.45 1574.34,1486.45 1577.46,1486.45 1580.57,1486.45 1583.69,1486.45 1586.8,1486.45 \n",
       "  1589.92,1486.45 1593.03,1486.45 1596.15,1486.45 1599.26,1486.45 1602.38,1486.45 1605.5,1486.45 1608.61,1486.45 1611.73,1486.45 1614.84,1486.45 1617.96,1486.45 \n",
       "  1621.07,1486.45 1624.19,1486.45 1627.3,1486.45 1630.42,1486.45 1633.53,1486.45 1636.65,1486.45 1639.76,1486.45 1642.88,1486.45 1645.99,1486.45 1649.11,1486.45 \n",
       "  1652.22,1486.45 1655.34,1486.45 1658.45,1486.45 1661.57,1486.45 1664.68,1486.45 1667.8,1486.45 1670.91,1486.45 1674.03,1486.45 1677.14,1486.45 1680.26,1486.45 \n",
       "  1683.37,1486.45 1686.49,1486.45 1689.6,1486.45 1692.72,1486.45 1695.83,1486.45 1698.95,1486.45 1702.06,1486.45 1705.18,1486.45 1708.29,1486.45 1711.41,1486.45 \n",
       "  1714.53,1486.45 1717.64,1486.45 1720.76,1486.45 1723.87,1486.45 1726.99,1486.45 1730.1,1486.45 1733.22,1486.45 1736.33,1486.45 1739.45,1486.45 1742.56,1486.45 \n",
       "  1745.68,1486.45 1748.79,1486.45 1751.91,1486.45 1755.02,1486.45 1758.14,1486.45 1761.25,1486.45 1764.37,1486.45 1767.48,1486.45 1770.6,1486.45 1773.71,1486.45 \n",
       "  1776.83,1486.45 1779.94,1486.45 1783.06,1486.45 1786.17,1486.45 1789.29,1486.45 1792.4,1486.45 1795.52,1486.45 1798.63,1486.45 1801.75,1486.45 1804.86,1486.45 \n",
       "  1807.98,1486.45 1811.09,1486.45 1814.21,1486.45 1817.32,1486.45 1820.44,1486.45 1823.56,1486.45 1826.67,1486.44 1829.79,1486.44 1832.9,1486.44 1836.02,1486.44 \n",
       "  1839.13,1486.43 1842.25,1486.42 1845.36,1486.42 1848.48,1486.4 1851.59,1486.39 1854.71,1486.36 1857.82,1486.33 1860.94,1486.29 1864.05,1486.23 1867.17,1486.16 \n",
       "  1870.28,1486.06 1873.4,1485.93 1876.51,1485.77 1879.63,1485.56 1882.74,1485.3 1885.86,1484.96 1888.97,1484.54 1892.09,1484.02 1895.2,1483.38 1898.32,1482.58 \n",
       "  1901.43,1481.62 1904.55,1480.45 1907.66,1479.04 1910.78,1477.36 1913.89,1475.36 1917.01,1473.01 1920.12,1470.26 1923.24,1467.06 1926.35,1463.37 1929.47,1459.14 \n",
       "  1932.59,1454.32 1935.7,1448.87 1938.82,1442.75 1941.93,1435.93 1945.05,1428.38 1948.16,1420.08 1951.28,1411.03 1954.39,1401.23 1957.51,1390.7 1960.62,1379.47 \n",
       "  1963.74,1367.58 1966.85,1355.11 1969.97,1342.12 1973.08,1328.71 1976.2,1314.99 1979.31,1301.09 1982.43,1287.14 1985.54,1273.28 1988.66,1259.68 1991.77,1246.48 \n",
       "  1994.89,1233.85 1998,1221.95 2001.12,1210.92 2004.23,1200.93 2007.35,1192.1 2010.46,1184.55 2013.58,1178.39 2016.69,1173.7 2019.81,1170.54 2022.92,1168.96 \n",
       "  2026.04,1168.96 2029.15,1170.53 2032.27,1173.66 2035.38,1178.28 2038.5,1184.33 2041.62,1191.7 2044.73,1200.28 2047.85,1209.96 2050.96,1220.59 2054.08,1232.04 \n",
       "  2057.19,1244.16 2060.31,1256.79 2063.42,1269.79 2066.54,1283.01 2069.65,1296.32 2072.77,1309.58 2075.88,1322.68 2079,1335.51 2082.11,1347.98 2085.23,1359.99 \n",
       "  2088.34,1371.49 2091.46,1382.41 2094.57,1392.72 2097.69,1402.39 2100.8,1411.39 2103.92,1419.73 2107.03,1427.41 2110.15,1434.43 2113.26,1440.82 2116.38,1446.6 \n",
       "  2119.49,1451.79 2122.61,1456.45 2125.72,1460.58 2128.84,1464.25 2131.95,1467.47 2135.07,1470.3 2138.18,1472.76 2141.3,1474.9 2144.42,1476.74 2147.53,1478.33 \n",
       "  2150.65,1479.68 2153.76,1480.83 2156.88,1481.81 2159.99,1482.63 2163.11,1483.32 2166.22,1483.89 2169.34,1484.37 2172.45,1484.77 2175.57,1485.09 2178.68,1485.36 \n",
       "  2181.8,1485.58 2184.91,1485.75 2188.03,1485.9 2191.14,1486.01 2194.26,1486.1 2197.37,1486.18 2200.49,1486.24 2203.6,1486.28 2206.72,1486.32 2209.83,1486.35 \n",
       "  2212.95,1486.37 2216.06,1486.39 2219.18,1486.4 2222.29,1486.41 2225.41,1486.42 2228.52,1486.43 2231.64,1486.43 2234.75,1486.44 2237.87,1486.44 2240.98,1486.44 \n",
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the NN-CME probabilities\n",
    "u0 = [1.; zeros(N)]; \n",
    "use_time=100.0; \n",
    "time_step = 2.0; \n",
    "tspan = (0.0, use_time);\n",
    "problem = ODEProblem(CME, u0, tspan, p1);\n",
    "\n",
    "sol = Array(solve(problem, Tsit5(), u0=u0, p=ps[1], saveat=0:time_step:Int(use_time)));\n",
    "\n",
    "# plot the selected snapshots\n",
    "bins = collect(0:N);\n",
    "f11 = plot(bins, [sol[:, 2] pdf.(Poisson(20*2), bins)], ylim=(0, 0.08), linewidth=[2 2], label=[\"NN-CME\" \"exact\"], title=\"time = 2s\");\n",
    "f12 = plot(bins, [sol[:, 4] pdf.(Poisson(20*6), bins)], ylim=(0, 0.05), linewidth=[2 2], label=[\"NN-CME\" \"exact\"], title=\"time = 6s\");\n",
    "f21 = plot(bins, [sol[:, 19] pdf.(Poisson(20*10), bins)], ylim=(0, 0.05), linewidth=[2 2], label=[\"NN-CME\" \"exact\"], title=\"time = 36s\");\n",
    "f22 = plot(bins, [sol[:, 29] pdf.(Poisson(20*10), bins)], ylim=(0, 0.05), linewidth=[2 2], label=[\"NN-CME\" \"exact\"], title=\"time = 56s\");\n",
    "plot(f11, f12, f21, f22, layout=(2,2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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