├── .gitattributes ├── README.md └── Poisson.ipynb /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Bayesian-PINN-Pytorch 2 | 3 | A simple Pytorch implementation of [Bayesian PINN](https://arxiv.org/abs/2003.06097) (HMC version). 4 | 5 | I use the Pytorch-based HMC package [hamiltorch](https://github.com/AdamCobb/hamiltorch). 6 | -------------------------------------------------------------------------------- /Poisson.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "218d03bf", 6 | "metadata": {}, 7 | "source": [ 8 | "A simple Pytorch code for Bayesian PINN using HMC. The governing equation is\n", 9 | "$0.01u_{xx} = f$, where $u = \\sin^3(6x)$. \n", 10 | "\n", 11 | "To install hamiltorch, type\n", 12 | "```\n", 13 | "pip install git+https://github.com/AdamCobb/hamiltorch\n", 14 | "```\n", 15 | "in your terminal." 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": 1, 21 | "id": "9678d6cd", 22 | "metadata": {}, 23 | "outputs": [], 24 | "source": [ 25 | "import torch\n", 26 | "import hamiltorch\n", 27 | "import matplotlib.pyplot as plt\n", 28 | "\n", 29 | "import torch.nn as nn\n", 30 | "import torch.nn.functional as F\n", 31 | "import numpy as np\n", 32 | "\n", 33 | "%matplotlib inline" 34 | ] 35 | }, 36 | { 37 | "cell_type": "code", 38 | "execution_count": 2, 39 | "id": "f60e33b6", 40 | "metadata": {}, 41 | "outputs": [], 42 | "source": [ 43 | "hamiltorch.set_random_seed(123)\n", 44 | "torch.manual_seed(123)\n", 45 | "np.random.seed(123)\n", 46 | "device = 'cpu'" 47 | ] 48 | }, 49 | { 50 | "cell_type": "code", 51 | "execution_count": 3, 52 | "id": "663d486f", 53 | "metadata": {}, 54 | "outputs": [], 55 | "source": [ 56 | "def generate(num, sigma, lam1, lam2):\n", 57 | " # positions\n", 58 | " lb = -0.7\n", 59 | " rb = 0.7\n", 60 | " X = np.linspace(lb, rb, num)[:,None]\n", 61 | " lb, rb = np.array([[lb]]), np.array([[rb]])\n", 62 | " # values (could be changed if needed)\n", 63 | " y = lam1 * (-1.08)*np.sin(6*X)*(\n", 64 | " np.sin(6*X)**2-2*np.cos(6*X)**2) \n", 65 | " X = np.concatenate([X, lb, rb], axis = 0)\n", 66 | " y = np.concatenate([y, np.sin(6*lb) ** 3 * lam2, np.sin(6*rb) ** 3 * lam2], axis = 0)\n", 67 | " y = y * (1 + sigma * np.random.randn(*y.shape))\n", 68 | " return X, y" 69 | ] 70 | }, 71 | { 72 | "cell_type": "code", 73 | "execution_count": 4, 74 | "id": "641dcfdb", 75 | "metadata": {}, 76 | "outputs": [], 77 | "source": [ 78 | "class PoissonPINN(torch.nn.Module):\n", 79 | " def __init__(self, width, lam1, lam2):\n", 80 | " super(PoissonPINN, self).__init__()\n", 81 | " self.fnn = nn.Sequential(\n", 82 | " nn.Linear(1, width),\n", 83 | " nn.Tanh(),\n", 84 | " nn.Linear(width, width),\n", 85 | " nn.Tanh(),\n", 86 | " nn.Linear(width, 1)\n", 87 | " )\n", 88 | " self.lam1 = lam1\n", 89 | " self.lam2 = lam2\n", 90 | " \n", 91 | " def forward(self, X):\n", 92 | " x = X[:-2].requires_grad_(True)\n", 93 | " u = self.fnn(x)\n", 94 | " u_x = torch.autograd.grad(u, x, grad_outputs = torch.ones_like(u), create_graph = True)[0]\n", 95 | " u_xx = torch.autograd.grad(u_x, x, grad_outputs = torch.ones_like(u), create_graph = True)[0]\n", 96 | " u_bd = self.fnn(X[-2:])\n", 97 | " return torch.cat([u_xx * self.lam1 * 0.01, u_bd * self.lam2], dim = 0)" 98 | ] 99 | }, 100 | { 101 | "cell_type": "code", 102 | "execution_count": 5, 103 | "id": "e1f583c0", 104 | "metadata": {}, 105 | "outputs": [], 106 | "source": [ 107 | "width = 50\n", 108 | "sigma = 0.01\n", 109 | "lam1 = 1/sigma\n", 110 | "lam2 = 1/sigma\n", 111 | "net = PoissonPINN(width, lam1, lam2)\n", 112 | "for param in net.parameters():\n", 113 | " torch.nn.init.normal_(param)" 114 | ] 115 | }, 116 | { 117 | "cell_type": "code", 118 | "execution_count": 6, 119 | "id": "638567ca", 120 | "metadata": {}, 121 | "outputs": [], 122 | "source": [ 123 | "train_num = 16\n", 124 | "test_num = 100\n", 125 | "\n", 126 | "X_train, y_train = generate(train_num, sigma, lam1, lam2)\n", 127 | "X_test, y_test = generate(test_num, 0, lam1, lam2)\n", 128 | "X_train = torch.FloatTensor(X_train)\n", 129 | "y_train = torch.FloatTensor(y_train)\n", 130 | "X_test = torch.FloatTensor(X_test)\n", 131 | "y_test = torch.FloatTensor(y_test)\n", 132 | " \n", 133 | "X_train = X_train.to(device)\n", 134 | "y_train = y_train.to(device)\n", 135 | "X_test = X_test.to(device)\n", 136 | "y_test = y_test.to(device)" 137 | ] 138 | }, 139 | { 140 | "cell_type": "code", 141 | "execution_count": 7, 142 | "id": "742be5ab", 143 | "metadata": {}, 144 | "outputs": [], 145 | "source": [ 146 | "tau_list = []\n", 147 | "tau = 1.#/100. # iris 1/10\n", 148 | "for w in net.parameters():\n", 149 | " tau_list.append(tau)\n", 150 | "tau_list = torch.tensor(tau_list).to(device)" 151 | ] 152 | }, 153 | { 154 | "cell_type": "code", 155 | "execution_count": 8, 156 | "id": "0ee07d6d", 157 | "metadata": {}, 158 | "outputs": [ 159 | { 160 | "name": "stdout", 161 | "output_type": "stream", 162 | "text": [ 163 | "Sampling (Sampler.HMC; Integrator.IMPLICIT)\n", 164 | "Time spent | Time remain.| Progress | Samples | Samples/sec\n", 165 | "0d:00:01:07 | 0d:00:00:00 | #################### | 5000/5000 | 73.86 \n", 166 | "Acceptance Rate 0.61\n" 167 | ] 168 | } 169 | ], 170 | "source": [ 171 | "params_init = hamiltorch.util.flatten(net).to(device).clone()\n", 172 | "\n", 173 | "# May need to tune step_size and L to make sure acceptance rate is around 0.5-0.8\n", 174 | "step_size = 0.0006\n", 175 | "burn = 2000\n", 176 | "num_samples = 5000\n", 177 | "L = 6\n", 178 | "params_hmc = hamiltorch.sample_model(net, X_train, y_train, model_loss='regression', params_init=params_init, num_samples=num_samples,\n", 179 | " step_size=step_size, burn = burn, num_steps_per_sample=L,tau_list=tau_list, tau_out=1)" 180 | ] 181 | }, 182 | { 183 | "cell_type": "code", 184 | "execution_count": 9, 185 | "id": "f675e18b", 186 | "metadata": {}, 187 | "outputs": [], 188 | "source": [ 189 | "y_pred_list = []\n", 190 | "for i in range(num_samples - burn):\n", 191 | " params = hamiltorch.util.unflatten(net, params_hmc[i])\n", 192 | " hamiltorch.util.update_model_params_in_place(net, params)\n", 193 | " y_pred = net(X_test)[:-2]\n", 194 | " y_pred_list.append(y_pred)\n", 195 | "y_pred = torch.stack(y_pred_list)" 196 | ] 197 | }, 198 | { 199 | "cell_type": "code", 200 | "execution_count": 10, 201 | "id": "b845c969", 202 | "metadata": {}, 203 | "outputs": [], 204 | "source": [ 205 | "y_mean = torch.mean(y_pred, dim = 0)\n", 206 | "y_std = torch.std(y_pred, dim = 0)\n", 207 | "y_up, y_low = y_mean - 2 * y_std, y_mean + 2 * y_std" 208 | ] 209 | }, 210 | { 211 | "cell_type": "code", 212 | "execution_count": 11, 213 | "id": "efbe210b", 214 | "metadata": {}, 215 | "outputs": [ 216 | { 217 | "data": { 218 | "text/plain": [ 219 | "Text(0.5, 0, 'x')" 220 | ] 221 | }, 222 | "execution_count": 11, 223 | "metadata": {}, 224 | "output_type": "execute_result" 225 | }, 226 | { 227 | "data": { 228 | "image/png": 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\n", 229 | "text/plain": [ 230 | "
" 231 | ] 232 | }, 233 | "metadata": { 234 | "needs_background": "light" 235 | }, 236 | "output_type": "display_data" 237 | } 238 | ], 239 | "source": [ 240 | "plt.plot(X_test[:-2].detach().cpu().numpy(), y_mean.detach().cpu().numpy(), label = 'mean')\n", 241 | "plt.plot(X_test[:-2].detach().cpu().numpy(), y_up.detach().cpu().numpy())\n", 242 | "plt.plot(X_test[:-2].detach().cpu().numpy(), y_low.detach().cpu().numpy())\n", 243 | "plt.plot(X_test[:-2].detach().cpu().numpy(), y_test[:-2].detach().cpu().numpy(), label = 'True')\n", 244 | "plt.scatter(X_train[:-2].detach().cpu().numpy(), y_train[:-2].detach().cpu().numpy(), label = 'Data')\n", 245 | "plt.legend()\n", 246 | "plt.ylabel('u_xx')\n", 247 | "plt.xlabel('x')" 248 | ] 249 | }, 250 | { 251 | "cell_type": "code", 252 | "execution_count": 12, 253 | "id": "4a9b3cbb", 254 | "metadata": {}, 255 | "outputs": [], 256 | "source": [ 257 | "u_pred_list = []\n", 258 | "for i in range(num_samples - burn):\n", 259 | " params = hamiltorch.util.unflatten(net, params_hmc[i])\n", 260 | " hamiltorch.util.update_model_params_in_place(net, params)\n", 261 | " u_pred = net.fnn(X_test)[:-2]\n", 262 | " u_pred_list.append(u_pred)\n", 263 | "u_pred = torch.stack(u_pred_list)" 264 | ] 265 | }, 266 | { 267 | "cell_type": "code", 268 | "execution_count": 13, 269 | "id": "e60719d5", 270 | "metadata": {}, 271 | "outputs": [], 272 | "source": [ 273 | "u_mean = torch.mean(u_pred, dim = 0)\n", 274 | "u_std = torch.std(u_pred, dim = 0)\n", 275 | "u_up, u_low = u_mean - 2 * u_std, u_mean + 2 * u_std" 276 | ] 277 | }, 278 | { 279 | "cell_type": "code", 280 | "execution_count": 14, 281 | "id": "f282ea4e", 282 | "metadata": {}, 283 | "outputs": [ 284 | { 285 | "data": { 286 | "text/plain": [ 287 | "Text(0.5, 0, 'x')" 288 | ] 289 | }, 290 | "execution_count": 14, 291 | "metadata": {}, 292 | "output_type": "execute_result" 293 | }, 294 | { 295 | "data": { 296 | "image/png": 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\n", 297 | "text/plain": [ 298 | "
" 299 | ] 300 | }, 301 | "metadata": { 302 | "needs_background": "light" 303 | }, 304 | "output_type": "display_data" 305 | } 306 | ], 307 | "source": [ 308 | "plt.plot(X_test[:-2].detach().cpu().numpy(), u_mean.detach().cpu().numpy(), label = 'mean')\n", 309 | "plt.plot(X_test[:-2].detach().cpu().numpy(), u_up.detach().cpu().numpy())\n", 310 | "plt.plot(X_test[:-2].detach().cpu().numpy(), u_low.detach().cpu().numpy())\n", 311 | "plt.plot(X_test[:-2].detach().cpu().numpy(), np.sin(X_test[:-2]*6)**3, label = 'True')\n", 312 | "plt.scatter(X_train[-2:].detach().cpu().numpy(), y_train[-2:].detach().cpu().numpy()/lam2, label = 'Data')\n", 313 | "plt.legend()\n", 314 | "plt.ylabel('u')\n", 315 | "plt.xlabel('x')" 316 | ] 317 | } 318 | ], 319 | "metadata": { 320 | "kernelspec": { 321 | "display_name": "Python 3", 322 | "language": "python", 323 | "name": "python3" 324 | }, 325 | "language_info": { 326 | "codemirror_mode": { 327 | "name": "ipython", 328 | "version": 3 329 | }, 330 | "file_extension": ".py", 331 | "mimetype": "text/x-python", 332 | "name": "python", 333 | "nbconvert_exporter": "python", 334 | "pygments_lexer": "ipython3", 335 | "version": "3.8.8" 336 | } 337 | }, 338 | "nbformat": 4, 339 | "nbformat_minor": 5 340 | } 341 | --------------------------------------------------------------------------------