{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple coupled ODE\n", "## Make sure you install the libraries\n", "\n", "## Execute the cells and the plots should be recreated\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import deepxde as dde\n", "import matplotlib.pyplot as plt\n", "from deepxde.backend import torch \n", "import numpy as np " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def pde(x,y):\n", " dy_xx = dde.grad.hessian(y, x, i=0, j=0)\n", " f = -2*torch.pi*(22-x)*torch.cos(2*torch.pi*x)+0.5*torch.sin(2*torch.pi*x)-torch.pi**2*(22-x)**2*torch.sin(2*torch.pi*x) + \\\n", " 2*8*torch.pi*(x-20)*torch.cos(2*8*torch.pi*x)+0.5*torch.sin(2*8*torch.pi*x)-8**2*torch.pi**2*(x-20)**2*torch.sin(2*8*torch.pi*x)\n", "\n", " res = dy_xx - f\n", " return res \n", "\n", "def func(x):\n", " return ((22-x)**2/4)*(np.sin(2*np.pi*x)) + ((x-20)**2/4)*(np.sin(16*np.pi*x))\n", "def func_plot(x):\n", " return ((22-x)**2/4)*(np.sin(2*np.pi*x)) + ((x-20)**2/4)*(np.sin(16*np.pi*x))\n", "x = np.linspace(20,22,100)\n", "\n", "u = func(x)\n", "plt.plot(x,u)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def output_transform(x,y):\n", " res = 0.0\n", " for n in range(1,10):\n", " res = res + y[:,n-1:n]*torch.sin(n*np.pi*x)\n", " return res\n", "def gauss_transform(x,y):\n", " res = 0.0\n", " for n in range(1,20):\n", "\n", " res = res + y[:,n-1:n]*torch.exp(-200*(x-0.05*n)*(x-0.05*n))\n", " return res" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "geom = dde.geometry.Interval(20, 22)\n", "\n", "\n", "bc = dde.icbc.DirichletBC(geom, func, lambda _, on_boundary: on_boundary)\n", "#ic_1 = dde.icbc.IC(geom, func, lambda _, on_initial: on_initial)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "data = dde.data.PDE(\n", " geom,\n", " pde,\n", " [bc],\n", " num_domain=1000,\n", " num_boundary=360,\n", " \n", " solution=func,\n", " num_test=1000,\n", ")\n", "\n", "layer_size = [1] + [50] * 4 + [1]\n", "activation = \"tanh\"\n", "initializer = \"Glorot uniform\"\n", "net = dde.nn.FNN(\n", " layer_size, activation, initializer\n", ")\n", "net.apply_feature_transform(lambda x: (x - 20)/2.0)\n", "#net.apply_output_transform(output_transform)\n", "\n", "\n", "\n", "\n", "layer_size_1 = [1] + [50] * 4 + [10]\n", "\n", "net1 = dde.nn.FNN(\n", " layer_size_1, activation, initializer\n", ")\n", "net1.apply_feature_transform(lambda x: (x - 20)/2.0)\n", "net1.apply_output_transform(output_transform)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Compiling model...\n", "'compile' took 0.000600 s\n", "\n", "Training model...\n", "\n", "Step Train loss Test loss Test metric \n", "0 [4.83e+05, 1.24e-02] [6.41e+05, 1.24e-02] [1.04e+00] \n", "1000 [1.00e+05, 2.35e+00] [1.33e+05, 2.35e+00] [5.41e+00] \n", "2000 [7.91e+04, 1.26e+00] [1.05e+05, 1.26e+00] [2.35e+00] \n", "3000 [7.97e+04, 2.46e+01] [1.05e+05, 2.46e+01] [1.24e+01] \n", "4000 [6.42e+04, 9.18e+00] [8.55e+04, 9.18e+00] [8.19e+00] \n", "5000 [4.95e+04, 1.51e+01] [6.59e+04, 1.51e+01] [9.41e+00] \n", "\n", "Best model at step 5000:\n", " train loss: 4.95e+04\n", " test loss: 6.59e+04\n", " test metric: [9.41e+00]\n", "\n", "'train' took 65.730943 s\n", "\n" ] } ], "source": [ "model = dde.Model(data, net)\n", "\n", "model.compile(\n", " \"adam\",\n", " lr=0.001,\n", " metrics=[\"l2 relative error\"],\n", " \n", ")\n", "losshistory, train_state = model.train(\n", " iterations=5000, display_every=1000\n", ")" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Compiling model...\n", "'compile' took 0.001819 s\n", "\n", "Training model...\n", "\n", "Step Train loss Test loss Test metric \n", "0 [4.87e+05, 3.02e-09] [6.47e+05, 3.02e-09] [1.12e+00] \n", "1000 [1.39e+05, 2.49e-09] [1.86e+05, 2.49e-09] [1.68e+00] \n", "2000 [2.15e+03, 4.90e-09] [2.88e+03, 4.90e-09] [2.82e-01] \n", "3000 [1.22e+03, 5.29e-09] [1.61e+03, 5.29e-09] [1.31e-01] \n", "4000 [4.23e+02, 5.40e-09] [5.78e+02, 5.40e-09] [4.45e-02] \n", "5000 [2.74e+02, 5.99e-09] [3.74e+02, 5.99e-09] [3.35e-02] \n", "\n", "Best model at step 5000:\n", " train loss: 2.74e+02\n", " test loss: 3.74e+02\n", " test metric: [3.35e-02]\n", "\n", "'train' took 120.968843 s\n", "\n" ] } ], "source": [ "model1 = dde.Model(data, net1)\n", "\n", "model1.compile(\n", " \"adam\",\n", " lr=0.001,\n", " metrics=[\"l2 relative error\"],\n", " \n", ")\n", "losshistory, train_state = model1.train(\n", " iterations=5000, display_every=1000\n", ")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "x_test= []\n", "for i in x:\n", " x_test.append([i])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "ypreds = model.predict(x_test)\n", "ypreds_1 = model1.predict(x_test)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,u,label=\"Ground Truth\",linestyle=\"dashed\")\n", "plt.plot(x,ypreds,label= \"Vanilla PINN\")\n", "plt.plot(x,ypreds_1,linestyle=\"dotted\",label=\"PINN - sinusoidal basis\",marker=\"*\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"u\")\n", "plt.legend()\n", "plt.savefig(\"sine_coupled.pdf\",dpi=500)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.17 ('newtorch')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.17" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "813e009bea45919a754463d31638190cf3c033fdb5fd5c2966a42653051a1217" } } }, "nbformat": 4, "nbformat_minor": 2 }