{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "2b714898", "metadata": {}, "outputs": [], "source": [ "import torch\n", "\n", "from pina.problem import SpatialProblem, TimeDependentProblem\n", "from pina.operators import laplacian, grad\n", "from pina.geometry import CartesianDomain\n", "from pina.solvers import PINN\n", "from pina.trainer import Trainer\n", "from pina.equation import Equation\n", "from pina.equation.equation_factory import FixedValue\n", "from pina import Condition, Plotter\n", "from pytorch_lightning.loggers import TensorBoardLogger\n", "from pina.model import FeedForward\n", "from pina.callbacks import MetricTracker" ] }, { "cell_type": "code", "execution_count": 2, "id": "6e9f489f", "metadata": {}, "outputs": [], "source": [ "class KleinGordon(TimeDependentProblem,SpatialProblem):\n", " output_variables = ['u']\n", " spatial_domain = CartesianDomain({'x':[-1,1],'y':[-1,1]})\n", " temporal_domain = CartesianDomain({'t': [0, 10]})\n", " def KG(input_,output_):\n", " u = output_.extract(['u'])\n", " x = input_.extract(['x'])\n", " y = input_.extract(['y'])\n", " t = input_.extract(['t'])\n", " u_t = grad(output_, input_, components=['u'], d=['t'])\n", " u_tt = grad(u_t, input_, components=['dudt'], d=['t'])\n", " nabla_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])\n", " temp = (x + y) * torch.cos(2*t) + (x * y) * torch.sin(2*t)\n", " f = temp**2 - 4*temp\n", " \n", " return u_tt - nabla_u + u**2 - f\n", " def boundary_condition(input_,output_):\n", " u = output_.extract(['u'])\n", " x = input_.extract(['x'])\n", " y = input_.extract(['y'])\n", " t = input_.extract(['t'])\n", " temp = (x + y) * torch.cos(2*t) + (x * y) * torch.sin(2*t)\n", " return u - temp\n", " \n", " \n", " def initial_condition(input_,output_):\n", " x = input_.extract(['x'])\n", " y = input_.extract(['y'])\n", " u_exp = x+y\n", " return output_.extract(['u']) - u_exp\n", " \n", " def kg_sol(self,pts):\n", " x = pts.extract(['x'])\n", " y = pts.extract(['y'])\n", " t = pts.extract(['t'])\n", " return (x + y) * torch.cos(2*t) + (x * y) * torch.sin(2*t)\n", " truth_solution = kg_sol\n", " \n", " conditions = {\n", " 'gamma1': Condition(location=CartesianDomain({'x': [-1, 1], 'y': 1, 't': [0, 10]}), equation=Equation(boundary_condition)),\n", " 'gamma2': Condition(location=CartesianDomain({'x': [-1, 1], 'y': -1, 't': [0, 10]}), equation=Equation(boundary_condition)),\n", " 'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [-1, 1], 't': [0, 10]}), equation=Equation(boundary_condition)),\n", " 'gamma4': Condition(location=CartesianDomain({'x': -1, 'y': [-1, 1], 't': [0, 10]}), equation=Equation(boundary_condition)),\n", " 't0': Condition(location=CartesianDomain({'x': [-1, 1], 'y': [-1, 1], 't': 0}), equation=Equation(initial_condition)),\n", " 'D': Condition(location=CartesianDomain({'x': [-1, 1], 'y': [-1, 1], 't': [0, 10]}), equation=Equation(KG)),\n", " }" ] }, { "cell_type": "code", "execution_count": 3, "id": "d8eb6c25", "metadata": {}, "outputs": [], "source": [ "problem = KleinGordon()" ] }, { "cell_type": "code", "execution_count": 4, "id": "db9d4097", "metadata": {}, "outputs": [], "source": [ "problem.discretise_domain(500, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])" ] }, { "cell_type": "code", "execution_count": 5, "id": "a47dcaea", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/vemuri/anaconda3/envs/pina/lib/python3.11/site-packages/lightning_fabric/plugins/environments/slurm.py:204: The `srun` command is available on your system but is not used. HINT: If your intention is to run Lightning on SLURM, prepend your python command with `srun` like so: srun python /home/vemuri/anaconda3/envs/pina/lib/python3.11/site ...\n", "GPU available: True (cuda), used: True\n", "TPU available: False, using: 0 TPU cores\n", "IPU available: False, using: 0 IPUs\n", "HPU available: False, using: 0 HPUs\n", "/home/vemuri/anaconda3/envs/pina/lib/python3.11/site-packages/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py:75: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `pytorch_lightning` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default\n", "LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n", "/home/vemuri/anaconda3/envs/pina/lib/python3.11/site-packages/pytorch_lightning/loops/fit_loop.py:298: The number of training batches (1) is smaller than the logging interval Trainer(log_every_n_steps=50). Set a lower value for log_every_n_steps if you want to see logs for the training epoch.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1: 0%| | 0/1 [00:00" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plotting at t=5\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plotting at t=10\n" ] }, { "data": { "image/png": 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AlwAAXiNvAN6jaeEb3nEPANbGR0IBfsa7GREonDQAANQij8As5A3gjp8knpR/2fsHugwACBreNmRpRLYsNCwAoAXg5AFgTXyXBcxAswJmIGsAxurR9VtO0AGwPKOuGLt7Hv4+hjYaFgAQwjh5AAAAzEbeABrHVRaBcfZCJz5aCwgAf73u6j4OzYvQQ8MC8CPe0Qh/4cQBEDq4ygJGIovASOQNwFxcZQHACgLdHKx9fP5ehg4aFgAQYjh5AAAAzETWADzDVRYAQlGgGxV3o3EROsLNmvi1116T4cOHS0xMjMTHx7t1H1WVxYsXS5cuXaRNmzaSnp4up06dchlTWloqEydOFJvNJvHx8TJ9+nQpLy834RkAxuIdjTBbZP55TiCEIE+Pp7du3ZL58+dLSkqKtG3bVpKSkmTy5Mny3//+1/xifUBuaFpZcligS0AIIIvACGSN4EVmaFwwZIafJJ706n7BdkLQSjhpCZijR9dvg/pvU7DXFyy8Oe795S9/kZEjR4rNZpOwsDC5cuVKg+M++ugjSUtLkzZt2kj79u3liSee8Kg20xoWlZWV8tRTT8msWbPcvs8bb7whf/rTn+Ttt9+W/fv3S9u2bWX06NFy48YN55iJEyfK8ePH5V//+pf885//lM8//1xmzpxpxlMAAMvg5EHo8vR4WlFRIUeOHJFFixbJkSNHZMuWLVJQUCCPP/64yZX6htwAmItmBXzFGyOCH5mhcWQGAPCd1RoB3ZMuBbqEoObNca+iokIyMjLk5ZdfbnTMP/7xD5k0aZJMmzZNjh49Kvv27ZMJEyZ4VFuYqpr6ocgbN26U2bNnN9pxqaWqkpSUJHPnzpWXXnpJREQcDockJCTIxo0bZfz48ZKfny8DBw6UgwcPygMPPCAiIrt27ZLHHntMLly4IElJSW7VdPXqVYmLi5PUSa9JRGS0T88PcBcnCmCGUDhxUFVTKZ98u14cDofYbDZD5679e5/eabq0Co80dO66zHwOtdw9njbk4MGDMnToUDl37px0797d+OIMFGy5oXYf6v3y/0hEdOAzA99lAW+RQ+CLYMobZh1zyQy3kRmMOdfw+y8fkejY1g2O8fajobhawDtWOrkK7/DaMJeVX0NV127KvrH/z7KZQcS83ODrcW/v3r3y8MMPy3fffedytWNVVZX06NFDli1bJtOnT/e6vqD5DouioiKx2+2Snp7u3BYXFydpaWmSnZ0t48ePl+zsbImPj3cupIhIenq6hIeHy/79++XnP/95g3PfvHlTbt688480h8MhIiLVlTcaHA8YzVZ0U6oCXQRCTmTBxZDYr6pqKkXk9j8mTXsMrRSpMW362/PL7eBSV1RUlERFRZn3wG5yOBwSFhbm9scmWIFZuaGxzFBzMzgyQ3UlDQt4jhwCb0UWXBQRCar9x+zcQGYgM9Ty5VzDzWuNv2qqrnnXQK65HhxZxGq8XW9YB68N83RPuiRV1wJdhfeqKqydGZyPIcbnBm+Pe805cuSIXLx4UcLDw2XIkCFit9slNTVVVq9eLYMGDXJ7nqBpWNjtdhERSUhIcNmekJDgvM1ut0vnzp1dbm/VqpV06NDBOaYhr7/+uixbtqze9rz/XeFr2QAAg1y+fFni4uIMnTMyMlISExNlr/3/GzpvQ2JjY6Vbt24u25YsWSJLly41/bGbcuPGDZk/f75kZmaa9k7OQDArNzSWGYr+sNyIsgEABjE6N5AZyAxGnmtYPeqzJira7WblMELwXB8GWE+ovH6snBlEzMkN3h73mnPmzBkREVm6dKmsXbtWevToIX/4wx9k5MiR8p///Ec6dOjg1jweNSwWLFggq1atanJMfn6+9O/v3SWOZlm4cKHMmTPH+fuVK1ckOTlZiouLDT85ZparV69Kt27d5Pz585YIj1arV4Sa/cFq9YpQsz84HA7p3r272wcuT0RHR0tRUZFUVlYaPvfdVFXCwly/GLmxdzz463h669Ytefrpp0VV5a233vJpLm9YMTeQGQLDajVbrV4RavYHq9UrYs2azcoNZAYygzfIDf5ntXpFrFez1eoVoWZ/sFq9IqGRGUTMyQ1mqam5fcnJK6+8IuPGjRMRkaysLOnatats3rxZnn32Wbfm8ahhMXfuXJk6dWqTY3r16uXJlE6JiYkiIlJSUiJdunRxbi8pKZHU1FTnmG+++cblflVVVVJaWuq8f0Mau0wmLi7OMi+yWjabzVI1W61eEWr2B6vVK0LN/hAeHm7KvNHR0RIdBN89UJeZx9NatScezp07J5999llA9gUr5gYyQ2BZrWar1StCzf5gtXpFrFmzGbmBzEBmqItzDcHNavWKWK9mq9UrQs3+YLV6RVpOZhBx/3jq7XGvObXH2YEDBzq3RUVFSa9evaS4uNjteTxqWHTq1Ek6dTLny2x69uwpiYmJ8umnnzpDw9WrV2X//v0ya9YsEREZNmyYXLlyRQ4fPiz333+/iIh89tlnUlNTI2lpaabUBQCA0cw8norcOfFw6tQp2bNnj3zve98z7bGaQm4AAMA3ZAbfkRkAAC2Fu8dTs457999/v0RFRUlBQYE8+OCDInI7a5w9e1aSk5Pdnsect7OKSHFxseTm5kpxcbFUV1dLbm6u5ObmSnl5uXNM//79ZevWrSIiEhYWJrNnz5ZXX31Vtm/fLnl5eTJ58mRJSkqSJ554QkREBgwYIBkZGTJjxgw5cOCA7Nu3T1544QUZP358s99eDgCAFXl6PL1165b84he/kEOHDsl7770n1dXVYrfbxW63++2SVW+QGwAA8A2ZgcwAAIA73DnuXbx4Ufr37y8HDhxw3s9ut0tubq4UFhaKiEheXp7k5uZKaWmpiNy+Aue5556TJUuWyO7du6WgoMD55oCnnnrK/QLVJFOmTFERqfezZ88e5xgR0aysLOfvNTU1umjRIk1ISNCoqCgdNWqUFhQUuMx7+fJlzczM1NjYWLXZbDpt2jQtKyvzqLYbN27okiVL9MaNG748Rb+yWs1Wq1eVmv3BavWqUrM/WK1ef/P0eFpUVNTg+LvvE2yCNTdYcf+kZvNZrV5VavYHq9WrSs2hhsywxzmGcw3us1rNVqtX1Xo1W61eVWr2B6vVq2rNmv2pueNebU6oe3xdsmRJg8fgusfcyspKnTt3rnbu3FnbtWun6enpeuzYMY9qC1NVdb+9AQAAAAAAAAAAYDzTPhIKAAAAAAAAAADAXTQsAAAAAAAAAABAwNGwAAAAAAAAAAAAAUfDAgAAAAAAAAAABFxINixee+01GT58uMTExEh8fLxb91FVWbx4sXTp0kXatGkj6enpcurUKZcxpaWlMnHiRLHZbBIfHy/Tp0+X8vJyQ2r2dO6zZ89KWFhYgz+bN292jmvo9k2bNgWkZhGRkSNH1qvnueeecxlTXFwsY8aMkZiYGOncubPMmzdPqqqq/F5vaWmp/PrXv5Z+/fpJmzZtpHv37vLiiy+Kw+FwGWfkGq9bt0569Ogh0dHRkpaWJgcOHGhy/ObNm6V///4SHR0tKSkpsmPHDpfb3dmvfeVJze+++6786Ec/kvbt20v79u0lPT293vipU6fWW8+MjIyA1bxx48Z69URHR7uMMXudPam3oddYWFiYjBkzxjnG7DX+/PPP5Wc/+5kkJSVJWFiYfPjhh83eZ+/evXLfffdJVFSU9OnTRzZu3FhvjKevD8BdVssNZIY7zMoM3tRMbjC2XjKDf2oOdG4gM8BqrJYZvJk70LmBzHBHS84MntYcDLmBzEBmgIE0BC1evFjXrl2rc+bM0bi4OLfus3LlSo2Li9MPP/xQjx49qo8//rj27NlTr1+/7hyTkZGh9957r3755Zf673//W/v06aOZmZmG1Ozp3FVVVfr111+7/CxbtkxjY2O1rKzMOU5ENCsry2Vc3efkz5pVVUeMGKEzZsxwqcfhcLg8r0GDBml6errm5OTojh07tGPHjrpw4UK/15uXl6dPPvmkbt++XQsLC/XTTz/Vvn376rhx41zGGbXGmzZt0sjISN2wYYMeP35cZ8yYofHx8VpSUtLg+H379mlERIS+8cYbeuLECf3973+vrVu31ry8POcYd/ZrX3ha84QJE3TdunWak5Oj+fn5OnXqVI2Li9MLFy44x0yZMkUzMjJc1rO0tNSQer2pOSsrS202m0s9drvdZYyZ6+xpvZcvX3ap9dixYxoREaFZWVnOMWav8Y4dO/SVV17RLVu2qIjo1q1bmxx/5swZjYmJ0Tlz5uiJEyf0zTff1IiICN21a5dzjKfrAHjCarmBzHDneZmVGbypmdxgbL1kBv/UHOjcQGaA1VgtM3gzd6BzA5nhjpaaGbypOdC5gcxwG5kBRgnJhkWtrKwst0JETU2NJiYm6urVq53brly5olFRUfr3v/9dVVVPnDihIqIHDx50jtm5c6eGhYXpxYsXfarTqLlTU1P1l7/8pcs2d17E3vC25hEjRuhvfvObRm/fsWOHhoeHu/yhfuutt9Rms+nNmzf9Xu/d3n//fY2MjNRbt245txm1xkOHDtXnn3/e+Xt1dbUmJSXp66+/3uD4p59+WseMGeOyLS0tTZ999llVdW+/9nfNd6uqqtJ27drpX//6V+e2KVOm6NixYw2pryGe1tzc3xGz19nXNf7jH/+o7dq10/Lycuc2s9e4LndeH7/73e/0nnvucdn2zDPP6OjRo52/+7oOgDuskBvIDHeYlRl8qflu5Abv670bmcGcmu8WyNxAZoCVWCEzGDm3v3IDmYHM4G3Nd/N3biAz3EZmgFFC8iOhPFVUVCR2u13S09Od2+Li4iQtLU2ys7NFRCQ7O1vi4+PlgQcecI5JT0+X8PBw2b9/v0+Pb8Tchw8fltzcXJk+fXq9255//nnp2LGjDB06VDZs2CCq6lO9vtb83nvvSceOHWXQoEGycOFCqaiocJk3JSVFEhISnNtGjx4tV69elePHjwek3rocDofYbDZp1aqVy3Zf17iyslIOHz7ssg+Gh4dLenq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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plotter = Plotter()\n", "\n", "# plotting at fixed time t = 0.0\n", "print('Plotting at t=0')\n", "plotter.plot(pinn, fixed_variables={'t': 0.0})\n", "\n", "# plotting at fixed time t = 0.5\n", "print('Plotting at t=5')\n", "plotter.plot(pinn, fixed_variables={'t':5})\n", "\n", "# plotting at fixed time t = 1.\n", "print('Plotting at t=10')\n", "plotter.plot(pinn, fixed_variables={'t': 10})" ] }, { "cell_type": "code", "execution_count": 14, "id": "ef9b0fcb", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "x = np.linspace(-1,1,100)\n", "y = np.linspace(-1,1,100)\n", "t = np.linspace(0,10,100)\n", "test_set = []\n", "for X in x:\n", " for Y in y:\n", " for T in t:\n", " test_set.append([X,Y,T])\n", " \n", "test_set = torch.Tensor(test_set) " ] }, { "cell_type": "markdown", "id": "44d9cde4", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 17, "id": "ff397a04", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "torch.Size([1000000, 3])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_set.shape" ] }, { "cell_type": "code", "execution_count": 16, "id": "0aaed6ac", "metadata": {}, "outputs": [], "source": [ "predicted_output= model(test_set).detach().numpy()\n", "def kg_sol(pts):\n", " x = pts[:,0]\n", " y = pts[:,1]\n", " t = pts[:,2]\n", " return (x + y) * torch.cos(2*t) + (x * y) * torch.sin(2*t)\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "6308ab81", "metadata": {}, "outputs": [], "source": [ "truth_output = kg_sol(test_set).detach().numpy().reshape((100**3,1))\n", "\n", "error = np.linalg.norm(predicted_output-truth_output) / np.linalg.norm(truth_output)" ] }, { "cell_type": "code", "execution_count": 19, "id": "61ab8f88", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000000, 1)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "truth_output.shape" ] }, { "cell_type": "code", "execution_count": 20, "id": "127968ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000000, 1)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predicted_output.shape" ] }, { "cell_type": "code", "execution_count": 21, "id": "8483904d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.07557773" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "error" ] }, { "cell_type": "markdown", "id": "a6ab97e4", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": null, "id": "e8c09bc9", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "pina", "language": "python", "name": "pina" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }