PINN Lightning.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2e0a6bf9",
   "metadata": {},
   "source": [
    "# PINN using functorch and pytorch Lightning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5dfb7b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "NOTE: Redirects are currently not supported in Windows or MacOs.\n"
     ]
    }
   ],
   "source": [
    "#importing\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.func as func\n",
    "import torchopt\n",
    "from torch.utils.data import DataLoader, random_split, TensorDataset\n",
    "import pytorch_lightning as pl\n",
    "import seaborn as sn\n",
    "import torchmetrics\n",
    "from torchmetrics import Metric\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.express as px\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "16a4f24f",
   "metadata": {},
   "source": [
    "## Loading the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "60f1fa1a",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>u</th>\n",
       "      <th>Hot gas pipe</th>\n",
       "      <th>Liquid pipe</th>\n",
       "      <th>Suction pipe</th>\n",
       "      <th>Door</th>\n",
       "      <th>Fridge</th>\n",
       "      <th>Environment</th>\n",
       "      <th>Energy</th>\n",
       "      <th>Water-1</th>\n",
       "      <th>Water-2</th>\n",
       "      <th>Water-3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>9.5</td>\n",
       "      <td>14.760000</td>\n",
       "      <td>24.6</td>\n",
       "      <td>24.4</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.7</td>\n",
       "      <td>24.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.76</td>\n",
       "      <td>14.76</td>\n",
       "      <td>14.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
       "      <td>14.780000</td>\n",
       "      <td>24.6</td>\n",
       "      <td>24.4</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.7</td>\n",
       "      <td>24.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.78</td>\n",
       "      <td>14.78</td>\n",
       "      <td>14.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>39.5</td>\n",
       "      <td>16.370000</td>\n",
       "      <td>24.6</td>\n",
       "      <td>24.4</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.7</td>\n",
       "      <td>24.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>16.37</td>\n",
       "      <td>16.37</td>\n",
       "      <td>16.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>9.5</td>\n",
       "      <td>14.771176</td>\n",
       "      <td>24.6</td>\n",
       "      <td>24.4</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.7</td>\n",
       "      <td>24.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.76</td>\n",
       "      <td>14.76</td>\n",
       "      <td>14.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
       "      <td>14.810000</td>\n",
       "      <td>24.6</td>\n",
       "      <td>24.4</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23.7</td>\n",
       "      <td>24.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>14.78</td>\n",
       "      <td>14.78</td>\n",
       "      <td>14.78</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   t   x     y          u  Hot gas pipe  Liquid pipe  Suction pipe  Door  \\\n",
       "0  0   4   9.5  14.760000          24.6         24.4          24.0   1.0   \n",
       "1  0  71  68.0  14.780000          24.6         24.4          24.0   1.0   \n",
       "2  0  22  39.5  16.370000          24.6         24.4          24.0   1.0   \n",
       "3  1   4   9.5  14.771176          24.6         24.4          24.0   1.0   \n",
       "4  1  71  68.0  14.810000          24.6         24.4          24.0   1.0   \n",
       "\n",
       "   Fridge  Environment  Energy  Water-1  Water-2  Water-3  \n",
       "0    23.7         24.9     0.0    14.76    14.76    14.76  \n",
       "1    23.7         24.9     0.0    14.78    14.78    14.78  \n",
       "2    23.7         24.9     0.0    16.37    16.37    16.37  \n",
       "3    23.7         24.9     0.0    14.76    14.76    14.76  \n",
       "4    23.7         24.9     0.0    14.78    14.78    14.78  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(22929, 14)\n",
      "tensor([[ 0.0000,  4.0000,  9.5000, 24.6000, 24.4000, 24.0000,  1.0000, 23.7000,\n",
      "         24.9000,  0.0000, 14.7600, 14.7600, 14.7600],\n",
      "        [ 0.0000, 71.0000, 68.0000, 24.6000, 24.4000, 24.0000,  1.0000, 23.7000,\n",
      "         24.9000,  0.0000, 14.7800, 14.7800, 14.7800]],\n",
      "       grad_fn=<SliceBackward0>)\n",
      "tensor([[14.7600],\n",
      "        [14.7800]])\n"
     ]
    }
   ],
   "source": [
    "# train data\n",
    "X = pd.read_csv('../Data/NN data/nn_train_mei_17-26.csv')\n",
    "X.drop(columns=[\"Unnamed: 0\"], inplace=True)\n",
    "X_input = X[['t', 'x', 'y', 'Hot gas pipe', 'Liquid pipe', 'Suction pipe', 'Door', \n",
    "             'Fridge', 'Environment', 'Energy', 'Water-1', 'Water-2', 'Water-3']]\n",
    "X_output = X[['u']]\n",
    "\n",
    "display(X.head())\n",
    "print(X.shape)\n",
    "# convert to Tensor\n",
    "X_input_tensor = torch.tensor(X_input.values, dtype=torch.float32, requires_grad=True)\n",
    "print(X_input_tensor[0:2])\n",
    "X_output_tensor = torch.tensor(X_output.values, dtype=torch.float32)\n",
    "print(X_output_tensor[0:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1a5a1f72",
   "metadata": {},
   "outputs": [
    {
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       "      <th>Hot gas pipe</th>\n",
       "      <th>Liquid pipe</th>\n",
       "      <th>Suction pipe</th>\n",
       "      <th>Door</th>\n",
       "      <th>Fridge</th>\n",
       "      <th>Environment</th>\n",
       "      <th>Energy</th>\n",
       "      <th>Water-1</th>\n",
       "      <th>Water-2</th>\n",
       "      <th>Water-3</th>\n",
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       "      <th>0</th>\n",
       "      <td>7643</td>\n",
       "      <td>22</td>\n",
       "      <td>39.5</td>\n",
       "      <td>6.854412</td>\n",
       "      <td>60.3</td>\n",
       "      <td>37.2</td>\n",
       "      <td>9.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-4.1</td>\n",
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       "      <td>37.2</td>\n",
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       "      <td>7.616774</td>\n",
       "      <td>7.400800</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7643</td>\n",
       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
       "      <td>7.751765</td>\n",
       "      <td>60.3</td>\n",
       "      <td>37.2</td>\n",
       "      <td>9.8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-4.1</td>\n",
       "      <td>27.8</td>\n",
       "      <td>950.0</td>\n",
       "      <td>7.576000</td>\n",
       "      <td>7.389706</td>\n",
       "      <td>7.185556</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7644</td>\n",
       "      <td>4</td>\n",
       "      <td>9.5</td>\n",
       "      <td>8.109630</td>\n",
       "      <td>62.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>6.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>27.1</td>\n",
       "      <td>850.0</td>\n",
       "      <td>7.947059</td>\n",
       "      <td>7.773143</td>\n",
       "      <td>7.616774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7644</td>\n",
       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
       "      <td>7.916000</td>\n",
       "      <td>62.1</td>\n",
       "      <td>35.7</td>\n",
       "      <td>6.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>27.1</td>\n",
       "      <td>850.0</td>\n",
       "      <td>7.751765</td>\n",
       "      <td>7.576000</td>\n",
       "      <td>7.389706</td>\n",
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      "text/plain": [
       "      t   x     y         u  Hot gas pipe  Liquid pipe  Suction pipe  Door  \\\n",
       "0  7643  22  39.5  6.854412          60.3         37.2           9.8   0.0   \n",
       "1  7643   4   9.5  7.947059          60.3         37.2           9.8   0.0   \n",
       "2  7643  71  68.0  7.751765          60.3         37.2           9.8   0.0   \n",
       "3  7644   4   9.5  8.109630          62.1         35.7           6.9   0.0   \n",
       "4  7644  71  68.0  7.916000          62.1         35.7           6.9   0.0   \n",
       "\n",
       "   Fridge  Environment  Energy   Water-1   Water-2   Water-3  \n",
       "0    -4.1         27.8   950.0  6.710571  6.585806  6.434194  \n",
       "1    -4.1         27.8   950.0  7.773143  7.616774  7.400800  \n",
       "2    -4.1         27.8   950.0  7.576000  7.389706  7.185556  \n",
       "3     0.9         27.1   850.0  7.947059  7.773143  7.616774  \n",
       "4     0.9         27.1   850.0  7.751765  7.576000  7.389706  "
      ]
     },
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     "output_type": "display_data"
    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7644, 14)\n"
     ]
    }
   ],
   "source": [
    "# validation data\n",
    "Y = pd.read_csv('../Data/NN data/nn_val_mei_17-26.csv')\n",
    "Y.drop(columns=[\"Unnamed: 0\"], inplace=True)\n",
    "Y_input = Y[['t', 'x', 'y', 'Hot gas pipe', 'Liquid pipe', 'Suction pipe', 'Door', \n",
    "             'Fridge', 'Environment', 'Energy', 'Water-1', 'Water-2', 'Water-3']]\n",
    "Y_output = Y[['u']]\n",
    "display(Y.head())\n",
    "print(Y.shape)\n",
    "\n",
    "# convert to Tensor\n",
    "Y_input_tensor = torch.tensor(Y_input.values, dtype=torch.float32)\n",
    "Y_output_tensor = torch.tensor(Y_output.values, dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c858985a",
   "metadata": {},
   "outputs": [
    {
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       "      <th>t</th>\n",
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       "      <th>Hot gas pipe</th>\n",
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       "      <th>1</th>\n",
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       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
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       "      <td>58.0</td>\n",
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       "      <td>3.250000</td>\n",
       "      <td>3.250000</td>\n",
       "      <td>3.190000</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10191</td>\n",
       "      <td>22</td>\n",
       "      <td>39.5</td>\n",
       "      <td>3.693429</td>\n",
       "      <td>58.0</td>\n",
       "      <td>33.3</td>\n",
       "      <td>6.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>26.0</td>\n",
       "      <td>650.0</td>\n",
       "      <td>3.771176</td>\n",
       "      <td>3.750000</td>\n",
       "      <td>3.699231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10192</td>\n",
       "      <td>71</td>\n",
       "      <td>68.0</td>\n",
       "      <td>3.220000</td>\n",
       "      <td>55.4</td>\n",
       "      <td>32.5</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.1</td>\n",
       "      <td>25.6</td>\n",
       "      <td>100.0</td>\n",
       "      <td>3.248235</td>\n",
       "      <td>3.250000</td>\n",
       "      <td>3.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10192</td>\n",
       "      <td>22</td>\n",
       "      <td>39.5</td>\n",
       "      <td>3.690000</td>\n",
       "      <td>55.4</td>\n",
       "      <td>32.5</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.1</td>\n",
       "      <td>25.6</td>\n",
       "      <td>100.0</td>\n",
       "      <td>3.693429</td>\n",
       "      <td>3.771176</td>\n",
       "      <td>3.750000</td>\n",
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      ],
      "text/plain": [
       "       t   x     y         u  Hot gas pipe  Liquid pipe  Suction pipe  Door  \\\n",
       "0  10191   4   9.5  3.683143          58.0         33.3           6.2   0.0   \n",
       "1  10191  71  68.0  3.248235          58.0         33.3           6.2   0.0   \n",
       "2  10191  22  39.5  3.693429          58.0         33.3           6.2   0.0   \n",
       "3  10192  71  68.0  3.220000          55.4         32.5           7.0   0.0   \n",
       "4  10192  22  39.5  3.690000          55.4         32.5           7.0   0.0   \n",
       "\n",
       "   Fridge  Environment  Energy   Water-1   Water-2   Water-3  \n",
       "0     0.6         26.0   650.0  3.690000  3.690000  3.676154  \n",
       "1     0.6         26.0   650.0  3.250000  3.250000  3.190000  \n",
       "2     0.6         26.0   650.0  3.771176  3.750000  3.699231  \n",
       "3     2.1         25.6   100.0  3.248235  3.250000  3.250000  \n",
       "4     2.1         25.6   100.0  3.693429  3.771176  3.750000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7644, 14)\n"
     ]
    }
   ],
   "source": [
    "# test data\n",
    "Z = pd.read_csv('../Data/NN data/nn_test_mei_17-26.csv')\n",
    "Z.drop(columns=['Unnamed: 0'], inplace=True)\n",
    "Z_input = Z[['t', 'x', 'y', 'Hot gas pipe', 'Liquid pipe', 'Suction pipe', 'Door', \n",
    "             'Fridge', 'Environment', 'Energy', 'Water-1', 'Water-2', 'Water-3']]\n",
    "Z_output = Z[['u']]\n",
    "\n",
    "display(Z.head())\n",
    "print(Z.shape)\n",
    "# convert to Tensor\n",
    "Z_input_tensor = torch.tensor(Z_input.values, dtype=torch.float32)\n",
    "Z_output_tensor = torch.tensor(Z_output.values, dtype=torch.float32)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "493fcde6",
   "metadata": {},
   "source": [
    "## Create NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3226c77e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NN(pl.LightningModule):\n",
    "    def __init__(self, input_size, output_size):\n",
    "        super().__init__()\n",
    "        self.model = nn.Sequential(\n",
    "            nn.Linear(input_size, 64),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(64, 64),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(64, output_size)\n",
    "        )\n",
    "\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "\n",
    "    def training_step(self, batch, batch_idx):\n",
    "        condition_losses = []\n",
    "\n",
    "        for condition_name, samples in batch.items():\n",
    "            condition = self.problem.conditions[condition_name]\n",
    "\n",
    "            # PINN loss: equation evaluated on location or input_points\n",
    "            if hasattr(condition, 'equation'):\n",
    "                target = condition.equation.residual(samples, self.forward(samples))\n",
    "                loss = self._loss(torch.zeros_like(target), target)\n",
    "            # PINN loss: evaluate model(input_points) vs output_points\n",
    "            elif hasattr(condition, 'output_points'):\n",
    "                input_pts, output_pts = samples\n",
    "                loss = self._loss(self.forward(input_pts), output_pts)\n",
    "\n",
    "            condition_losses.append(loss * condition.data_weight)\n",
    "\n",
    "        # TODO Fix the bug, tot_loss is a label tensor without labels\n",
    "        # we need to pass it as a torch tensor to make everything work\n",
    "        total_loss = sum(condition_losses)\n",
    "        return total_loss\n",
    "\n",
    "    def validation_step(self, batch, batch_idx):\n",
    "        x, y = batch\n",
    "        y_hat = self.model(x)\n",
    "        loss = self.loss(y_hat, y)\n",
    "        self.log('val_loss', loss)\n",
    "        return loss\n",
    "\n",
    "    def test_step(self, batch, batch_idx):\n",
    "        x, y = batch\n",
    "        y_hat = self.model(x)\n",
    "        loss = self.loss(y_hat, y)\n",
    "        self.log('test_loss', loss)\n",
    "        return loss\n",
    "    \n",
    "    def configure_optimizers(self, lr=1e-3):\n",
    "        return torch.optim.Adam(self.parameters(), lr=lr)\n",
    "\n",
    "    def train_dataloader(self, batchsize=64):\n",
    "        return DataLoader(TensorDataset(X_input_tensor, X_output_tensor), batch_size=batchsize, shuffle=True)\n",
    "    \n",
    "    def val_dataloader(self, batchsize=64):\n",
    "        return DataLoader(TensorDataset(Y_input_tensor, Y_output_tensor), batch_size=batchsize, shuffle=False)\n",
    "    \n",
    "    def test_dataloader(self, batchsize=64):\n",
    "        return DataLoader(TensorDataset(Z_input_tensor, Z_output_tensor), batch_size=batchsize, shuffle=False)\n",
    "    "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "b9c6863e",
   "metadata": {},
   "source": [
    "## Define PDE, Boundary and initial condition losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f627bcea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 4., 71., 22.,  ..., 71., 22.,  4.], grad_fn=<SelectBackward0>)\n"
     ]
    }
   ],
   "source": [
    "input_size = X_input.shape[1]\n",
    "output_size = X_output.shape[1]\n",
    "\n",
    "# create the PINN model and make it functional using functorch utilities\n",
    "model = NN(input_size=input_size, output_size=output_size)\n",
    "\n",
    "x = X_input_tensor\n",
    "print(x[:, 1])\n",
    "def loss_fn(pred: torch.Tensor, target: torch.Tensor):\n",
    "    # PDE loss\n",
    "\n",
    "    # compute derivative of the prediction with respect to x\n",
    "    pred_x = torch.autograd.grad(pred, x, torch.ones_like(pred), create_graph=True)[0]\n",
    "    \n",
    "    \n",
    "\n",
    "    # compute second order derivatives\n",
    "\n",
    "\n",
    "    # boundary loss\n",
    "\n",
    "\n",
    "    loss_NN = nn.MSELoss()(pred, target)\n",
    "\n",
    "    loss_value = loss_NN\n",
    "\n",
    "    return loss_value\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "4a0ca795",
   "metadata": {},
   "source": [
    "## Train and validate the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8c73d920",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: False, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "IPU available: False, using: 0 IPUs\n",
      "HPU available: False, using: 0 HPUs\n",
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py:67: UserWarning: 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",
      "  warning_cache.warn(\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 5.1 K \n",
      "-------------------------------------\n",
      "5.1 K     Trainable params\n",
      "0         Non-trainable params\n",
      "5.1 K     Total params\n",
      "0.020     Total estimated model params size (MB)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sanity Checking DataLoader 0:   0%|          | 0/2 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/connectors/data_connector.py:430: PossibleUserWarning: The dataloader, val_dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 4 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  rank_zero_warn(\n"
     ]
    },
    {
     "ename": "RuntimeError",
     "evalue": "element 0 of tensors does not require grad and does not have a grad_fn",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-686e873284ae>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;31m# initialize trainer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0mtrainer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTrainer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmax_epochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnum_epochs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccelerator\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'cpu'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m \u001b[0mtrainer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrain_loader\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval_loader\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/trainer.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, model, train_dataloaders, val_dataloaders, datamodule, ckpt_path)\u001b[0m\n\u001b[1;32m    518\u001b[0m         \u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_maybe_unwrap_optimized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    519\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstrategy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_lightning_module\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 520\u001b[0;31m         call._call_and_handle_interrupt(\n\u001b[0m\u001b[1;32m    521\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_fit_impl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrain_dataloaders\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval_dataloaders\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdatamodule\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mckpt_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    522\u001b[0m         )\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/call.py\u001b[0m in \u001b[0;36m_call_and_handle_interrupt\u001b[0;34m(trainer, trainer_fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m     42\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mtrainer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstrategy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlauncher\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlaunch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrainer_fn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrainer\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtrainer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 44\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mtrainer_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     45\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0m_TunerExitException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/trainer.py\u001b[0m in \u001b[0;36m_fit_impl\u001b[0;34m(self, model, train_dataloaders, val_dataloaders, datamodule, ckpt_path)\u001b[0m\n\u001b[1;32m    557\u001b[0m             \u001b[0mmodel_connected\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlightning_module\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    558\u001b[0m         )\n\u001b[0;32m--> 559\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mckpt_path\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mckpt_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    560\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    561\u001b[0m         \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstopped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/trainer.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self, model, ckpt_path)\u001b[0m\n\u001b[1;32m    933\u001b[0m         \u001b[0;31m# RUN THE TRAINER\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    934\u001b[0m         \u001b[0;31m# ----------------------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 935\u001b[0;31m         \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run_stage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    936\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    937\u001b[0m         \u001b[0;31m# ----------------------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/trainer.py\u001b[0m in \u001b[0;36m_run_stage\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    974\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraining\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    975\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0misolate_rng\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 976\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run_sanity_check\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    977\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautograd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_detect_anomaly\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_detect_anomaly\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    978\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit_loop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/trainer.py\u001b[0m in \u001b[0;36m_run_sanity_check\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1003\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1004\u001b[0m             \u001b[0;31m# run eval step\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1005\u001b[0;31m             \u001b[0mval_loop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1006\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1007\u001b[0m             \u001b[0mcall\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_callback_hooks\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"on_sanity_check_end\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/loops/utilities.py\u001b[0m in \u001b[0;36m_decorator\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    175\u001b[0m             \u001b[0mcontext_manager\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_grad\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    176\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mcontext_manager\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 177\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mloop_run\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    178\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    179\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0m_decorator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/loops/evaluation_loop.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    113\u001b[0m                 \u001b[0mprevious_dataloader_idx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdataloader_idx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    114\u001b[0m                 \u001b[0;31m# run step hooks\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 115\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_evaluation_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_idx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdataloader_idx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    116\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    117\u001b[0m                 \u001b[0;31m# this needs to wrap the `*_step` call too (not just `next`) for `dataloader_iter` support\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/loops/evaluation_loop.py\u001b[0m in \u001b[0;36m_evaluation_step\u001b[0;34m(self, batch, batch_idx, dataloader_idx)\u001b[0m\n\u001b[1;32m    373\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    374\u001b[0m         \u001b[0mhook_name\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"test_step\"\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mtrainer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtesting\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m\"validation_step\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 375\u001b[0;31m         \u001b[0moutput\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcall\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_strategy_hook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrainer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhook_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mstep_kwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    376\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    377\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbatch_progress\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mincrement_processed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/call.py\u001b[0m in \u001b[0;36m_call_strategy_hook\u001b[0;34m(trainer, hook_name, *args, **kwargs)\u001b[0m\n\u001b[1;32m    286\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    287\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mtrainer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprofiler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprofile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"[Strategy]{trainer.strategy.__class__.__name__}.{hook_name}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 288\u001b[0;31m         \u001b[0moutput\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    289\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    290\u001b[0m     \u001b[0;31m# restore current_fx when nested context\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/strategies/strategy.py\u001b[0m in \u001b[0;36mvalidation_step\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    376\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprecision_plugin\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mval_step_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    377\u001b[0m             \u001b[0;32massert\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mValidationStep\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 378\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalidation_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    379\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    380\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mtest_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mAny\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mAny\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mOptional\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mSTEP_OUTPUT\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-6-59d663ce577d>\u001b[0m in \u001b[0;36mvalidation_step\u001b[0;34m(self, batch, batch_idx)\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbatch\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m         \u001b[0my_hat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m         \u001b[0mloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloss\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_hat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'val_loss'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mloss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-7-4f2ac58ae49e>\u001b[0m in \u001b[0;36mloss_fn\u001b[0;34m(pred, target)\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m     \u001b[0;31m# compute derivative of the prediction with respect to x\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m     \u001b[0mpred_x\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautograd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones_like\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpred\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36mgrad\u001b[0;34m(outputs, inputs, grad_outputs, retain_graph, create_graph, only_inputs, allow_unused, is_grads_batched)\u001b[0m\n\u001b[1;32m    301\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_vmap_internals\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_vmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mallow_none_pass_through\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrad_outputs_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    302\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 303\u001b[0;31m         return Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass\n\u001b[0m\u001b[1;32m    304\u001b[0m             \u001b[0mt_outputs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_outputs_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_inputs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    305\u001b[0m             allow_unused, accumulate_grad=False)  # Calls into the C++ engine to run the backward pass\n",
      "\u001b[0;31mRuntimeError\u001b[0m: element 0 of tensors does not require grad and does not have a grad_fn"
     ]
    }
   ],
   "source": [
    "# Parameters\n",
    "input_size = X_input.shape[1]\n",
    "output_size = X_output.shape[1]\n",
    "learning_rate = 0.001\n",
    "batch_size = 64\n",
    "num_epochs = 10\n",
    "\n",
    "# Loss\n",
    "model.loss = loss_fn\n",
    "\n",
    "# Data\n",
    "train_loader = model.train_dataloader(batch_size)\n",
    "val_loader = model.val_dataloader(batch_size)\n",
    "test_loader = model.test_dataloader(batch_size)\n",
    "\n",
    "# initialize trainer\n",
    "trainer = pl.Trainer(max_epochs=num_epochs, accelerator='cpu')\n",
    "trainer.fit(model, train_loader, val_loader)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ec5df27a",
   "metadata": {},
   "source": [
    "## Testing and evaluating the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "96fda753",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/connectors/checkpoint_connector.py:148: UserWarning: `.test(ckpt_path=None)` was called without a model. The best model of the previous `fit` call will be used. You can pass `.test(ckpt_path='best')` to use the best model or `.test(ckpt_path='last')` to use the last model. If you pass a value, this warning will be silenced.\n",
      "  rank_zero_warn(\n",
      "Restoring states from the checkpoint path at /Users/Bo/Desktop/School/Jaar3/Scriptie/Code/lightning_logs/version_58/checkpoints/epoch=9-step=3590.ckpt\n",
      "Loaded model weights from the checkpoint at /Users/Bo/Desktop/School/Jaar3/Scriptie/Code/lightning_logs/version_58/checkpoints/epoch=9-step=3590.ckpt\n",
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/pytorch_lightning/trainer/connectors/data_connector.py:430: PossibleUserWarning: The dataloader, test_dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 4 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  rank_zero_warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing DataLoader 0: 100%|██████████| 120/120 [00:01<00:00, 117.48it/s]\n"
     ]
    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\">        Test metric        </span>┃<span style=\"font-weight: bold\">       DataLoader 0        </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\">         test_loss         </span>│<span style=\"color: #800080; text-decoration-color: #800080\">    0.6083737015724182     </span>│\n",
       "└───────────────────────────┴───────────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1m       Test metric       \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m      DataLoader 0       \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│\u001b[36m \u001b[0m\u001b[36m        test_loss        \u001b[0m\u001b[36m \u001b[0m│\u001b[35m \u001b[0m\u001b[35m   0.6083737015724182    \u001b[0m\u001b[35m \u001b[0m│\n",
       "└───────────────────────────┴───────────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[{'test_loss': 0.6083737015724182}]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test model\n",
    "trainer.test()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c410f918",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>train_loss</th>\n",
       "      <th>val_loss</th>\n",
       "      <th>test_loss</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>epoch</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>39.306480</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>0</th>\n",
       "      <td>3.987778</td>\n",
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       "      <td>NaN</td>\n",
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       "      <th>0</th>\n",
       "      <td>1.401397</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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      ],
      "text/plain": [
       "       train_loss  val_loss  test_loss\n",
       "epoch                                 \n",
       "0       39.306480       NaN        NaN\n",
       "0        3.987778       NaN        NaN\n",
       "0        1.401397       NaN        NaN\n",
       "0        1.368974       NaN        NaN\n",
       "0        1.502220       NaN        NaN"
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    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7fcfb54d8d90>"
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     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 443.75x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "metrics = pd.read_csv(f\"{trainer.logger.log_dir}/metrics.csv\")\n",
    "del metrics[\"step\"]\n",
    "metrics.set_index(\"epoch\", inplace=True)\n",
    "display(metrics.dropna(axis=1, how=\"all\").head())\n",
    "sn.relplot(data=metrics, kind=\"line\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "995f83be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 0.60837376\n"
     ]
    },
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
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   "source": [
    "# predict\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(Z_input_tensor)\n",
    "    loss = model.loss(y_pred, Z_output_tensor)\n",
    "    print(f\"Loss: {loss:.8f}\")\n",
    "\n",
    "# tensor to numpy\n",
    "prediction_values = y_pred.numpy()\n",
    "true_values = Z_output_tensor.numpy()\n",
    "\n",
    "# plot\n",
    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter(x=list(range(len(true_values))), y=true_values.flatten(), mode='lines', name='True'))\n",
    "fig.add_trace(go.Scatter(x=list(range(len(prediction_values))), y=prediction_values.flatten(), mode='lines', name='Prediction'))\n",
    "fig.update_layout(title='Prediction vs True', xaxis_title='Time', yaxis_title='Temperature')\n",
    "fig.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "fb52e9b3",
   "metadata": {},
   "source": [
    "### Functorch stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9d97645f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NN(nn.Module):\n",
    "    def __init__(\n",
    "        self,\n",
    "        num_inputs: int = 1,\n",
    "        num_outputs: int = 1,\n",
    "        num_hidden: int = 1,\n",
    "        dim_hidden: int = 1,\n",
    "        act: nn.Module = nn.Tanh(),\n",
    "    ) -> None:\n",
    "        \"\"\"Simple neural network with linear layers and non-linear activation function\n",
    "        This class is used as universal function approximator for the solution of\n",
    "        partial differential equations using PINNs\n",
    "        Args:\n",
    "            num_inputs (int, optional): The number of input dimensions\n",
    "            num_outputs (int, optional): The number of outputs of the model, in general is 1\n",
    "            num_hidden (int, optional): The number of hidden layers in the model\n",
    "            dim_hidden (int, optional): The number of neurons for each hidden layer\n",
    "            act (nn.Module, optional): The type of non-linear activation function to be used\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "\n",
    "        self.layer_in = nn.Linear(num_inputs, dim_hidden)\n",
    "        self.layer_out = nn.Linear(dim_hidden, num_outputs)\n",
    "\n",
    "        num_middle = num_hidden - 1\n",
    "        self.middle_layers = nn.ModuleList(\n",
    "            [nn.Linear(dim_hidden, dim_hidden) for _ in range(num_middle)]\n",
    "        )\n",
    "        self.act = act\n",
    "\n",
    "        self.num_inputs = num_inputs\n",
    "        self.num_outputs = num_outputs\n",
    "\n",
    "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
    "        out = self.act(self.layer_in(x))\n",
    "        for layer in self.middle_layers:\n",
    "            out = self.act(layer(out))\n",
    "        return self.layer_out(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d0804cb3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/torch/_functorch/deprecated.py:97: UserWarning:\n",
      "\n",
      "We've integrated functorch into PyTorch. As the final step of the integration, functorch.make_functional is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use torch.func.functional_call instead; see the PyTorch 2.0 release notes and/or the torch.func migration guide for more details https://pytorch.org/docs/master/func.migrating.html\n",
      "\n",
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/torch/_functorch/deprecated.py:58: UserWarning:\n",
      "\n",
      "We've integrated functorch into PyTorch. As the final step of the integration, functorch.vmap is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use torch.vmap instead; see the PyTorch 2.0 release notes and/or the torch.func migration guide for more details https://pytorch.org/docs/master/func.migrating.html\n",
      "\n",
      "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/torch/_functorch/deprecated.py:62: UserWarning:\n",
      "\n",
      "We've integrated functorch into PyTorch. As the final step of the integration, functorch.grad is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use torch.func.grad instead; see the PyTorch 2.0 release notes and/or the torch.func migration guide for more details https://pytorch.org/docs/master/func.migrating.html\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from functorch import make_functional, grad, vmap\n",
    "\n",
    "# create the PINN model and make it functional using functorch utilities\n",
    "model = NN()\n",
    "fmodel, params = make_functional(model)\n",
    "\n",
    "def f(x: torch.Tensor, params: torch.Tensor) -> torch.Tensor:\n",
    "    # only a single element is supported thus unsqueeze must be applied\n",
    "    # for batching multiple inputs, `vmap` must be used as below\n",
    "    x_ = x.unsqueeze(0)\n",
    "    res = fmodel(params, x_).squeeze(0)\n",
    "    return res\n",
    "\n",
    "# use `vmap` primitive to allow efficient batching of the input\n",
    "f_vmap = vmap(f, in_dims=(0, None))\n",
    "\n",
    "# return function for computing higher order gradients with respect\n",
    "# to input by simply composing `grad` calls and use again `vmap` for\n",
    "# efficient batching of the input\n",
    "dfdx = vmap(grad(f), in_dims=(0, None))\n",
    "d2fdx2 = vmap(grad(grad(f)), in_dims=(0, None))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ad5bd19a",
   "metadata": {},
   "outputs": [],
   "source": [
    "R = 1.0  # rate of maximum population growth parameterizing the equation\n",
    "X_BOUNDARY = 0.0  # boundary condition coordinate\n",
    "F_BOUNDARY = 0.5  # boundary condition value\n",
    "\n",
    "\n",
    "def loss_fn(params: torch.Tensor, x: torch.Tensor) -> torch.Tensor:\n",
    "\n",
    "    # interior loss\n",
    "    f_value = f_vmap(x, params)\n",
    "    interior = dfdx(x, params) - R * f_value * (1 - f_value)\n",
    "\n",
    "    # boundary loss\n",
    "    x0 = X_BOUNDARY\n",
    "    f0 = F_BOUNDARY\n",
    "    x_boundary = torch.tensor([x0])\n",
    "    f_boundary = torch.tensor([f0])\n",
    "    boundary = f_vmap(x_boundary, params) - f_boundary\n",
    "\n",
    "    loss = nn.MSELoss()\n",
    "    loss_value = loss(interior, torch.zeros_like(interior)) + loss(\n",
    "        boundary, torch.zeros_like(boundary)\n",
    "    )\n",
    "\n",
    "    return loss_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c279fd22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 with loss 3.1161837577819824\n",
      "Iteration 1 with loss 1.7665841579437256\n",
      "Iteration 2 with loss 0.9638484716415405\n",
      "Iteration 3 with loss 0.5573378205299377\n",
      "Iteration 4 with loss 0.26031291484832764\n",
      "Iteration 5 with loss 0.1401580572128296\n",
      "Iteration 6 with loss 0.09672214090824127\n",
      "Iteration 7 with loss 0.07434478402137756\n",
      "Iteration 8 with loss 0.08948375284671783\n",
      "Iteration 9 with loss 0.10277165472507477\n",
      "Iteration 10 with loss 0.13193379342556\n",
      "Iteration 11 with loss 0.1359812617301941\n",
      "Iteration 12 with loss 0.19631457328796387\n",
      "Iteration 13 with loss 0.21327154338359833\n",
      "Iteration 14 with loss 0.24476897716522217\n",
      "Iteration 15 with loss 0.25221559405326843\n",
      "Iteration 16 with loss 0.25393447279930115\n",
      "Iteration 17 with loss 0.24947024881839752\n",
      "Iteration 18 with loss 0.23438483476638794\n",
      "Iteration 19 with loss 0.21325591206550598\n",
      "Iteration 20 with loss 0.18858323991298676\n",
      "Iteration 21 with loss 0.1632629930973053\n",
      "Iteration 22 with loss 0.1393880695104599\n",
      "Iteration 23 with loss 0.11819514632225037\n",
      "Iteration 24 with loss 0.10028022527694702\n",
      "Iteration 25 with loss 0.08518550544977188\n",
      "Iteration 26 with loss 0.07401026785373688\n",
      "Iteration 27 with loss 0.06417346000671387\n",
      "Iteration 28 with loss 0.0572340190410614\n",
      "Iteration 29 with loss 0.05219448730349541\n",
      "Iteration 30 with loss 0.04802209883928299\n",
      "Iteration 31 with loss 0.05032329633831978\n",
      "Iteration 32 with loss 0.04573490843176842\n",
      "Iteration 33 with loss 0.03582661598920822\n",
      "Iteration 34 with loss 0.04197053983807564\n",
      "Iteration 35 with loss 0.06167992204427719\n",
      "Iteration 36 with loss 0.06434046477079391\n",
      "Iteration 37 with loss 0.060729071497917175\n",
      "Iteration 38 with loss 0.057015158236026764\n",
      "Iteration 39 with loss 0.05099111050367355\n",
      "Iteration 40 with loss 0.0477544441819191\n",
      "Iteration 41 with loss 0.054926395416259766\n",
      "Iteration 42 with loss 0.04772588610649109\n",
      "Iteration 43 with loss 0.05192568898200989\n",
      "Iteration 44 with loss 0.057460445910692215\n",
      "Iteration 45 with loss 0.05230932682752609\n",
      "Iteration 46 with loss 0.04881351441144943\n",
      "Iteration 47 with loss 0.04260653629899025\n",
      "Iteration 48 with loss 0.04419257119297981\n",
      "Iteration 49 with loss 0.037748321890830994\n",
      "Iteration 50 with loss 0.04195307940244675\n",
      "Iteration 51 with loss 0.04078701511025429\n",
      "Iteration 52 with loss 0.04568914324045181\n",
      "Iteration 53 with loss 0.03809304162859917\n",
      "Iteration 54 with loss 0.040010966360569\n",
      "Iteration 55 with loss 0.04044310748577118\n",
      "Iteration 56 with loss 0.04358057677745819\n",
      "Iteration 57 with loss 0.04178941622376442\n",
      "Iteration 58 with loss 0.04133211821317673\n",
      "Iteration 59 with loss 0.041266679763793945\n",
      "Iteration 60 with loss 0.04035983979701996\n",
      "Iteration 61 with loss 0.03893978148698807\n",
      "Iteration 62 with loss 0.04242449998855591\n",
      "Iteration 63 with loss 0.03943007439374924\n",
      "Iteration 64 with loss 0.044676728546619415\n",
      "Iteration 65 with loss 0.04162312671542168\n",
      "Iteration 66 with loss 0.04261064529418945\n",
      "Iteration 67 with loss 0.04399358108639717\n",
      "Iteration 68 with loss 0.032591864466667175\n",
      "Iteration 69 with loss 0.0398927740752697\n",
      "Iteration 70 with loss 0.042678941041231155\n",
      "Iteration 71 with loss 0.03841889649629593\n",
      "Iteration 72 with loss 0.04013790562748909\n",
      "Iteration 73 with loss 0.027399571612477303\n",
      "Iteration 74 with loss 0.03832921385765076\n",
      "Iteration 75 with loss 0.03311619535088539\n",
      "Iteration 76 with loss 0.03033154085278511\n",
      "Iteration 77 with loss 0.03921022638678551\n",
      "Iteration 78 with loss 0.03540616109967232\n",
      "Iteration 79 with loss 0.0398130863904953\n",
      "Iteration 80 with loss 0.03216668218374252\n",
      "Iteration 81 with loss 0.03920687362551689\n",
      "Iteration 82 with loss 0.03910931944847107\n",
      "Iteration 83 with loss 0.040623150765895844\n",
      "Iteration 84 with loss 0.038596268743276596\n",
      "Iteration 85 with loss 0.03283742815256119\n",
      "Iteration 86 with loss 0.03762936219573021\n",
      "Iteration 87 with loss 0.042459264397621155\n",
      "Iteration 88 with loss 0.03786610811948776\n",
      "Iteration 89 with loss 0.0399387925863266\n",
      "Iteration 90 with loss 0.03469318524003029\n",
      "Iteration 91 with loss 0.03621966019272804\n",
      "Iteration 92 with loss 0.03977307677268982\n",
      "Iteration 93 with loss 0.03459280729293823\n",
      "Iteration 94 with loss 0.035394128412008286\n",
      "Iteration 95 with loss 0.035277243703603745\n",
      "Iteration 96 with loss 0.039548974484205246\n",
      "Iteration 97 with loss 0.03666665032505989\n",
      "Iteration 98 with loss 0.038925960659980774\n",
      "Iteration 99 with loss 0.03443401679396629\n"
     ]
    }
   ],
   "source": [
    "# choose the configuration\n",
    "batch_size = 30  # number of colocation points sampled in the domain\n",
    "num_iter = 100  # maximum number of iterations\n",
    "learning_rate = 1e-1  # learning rate\n",
    "domain = (-5.0, 5.0)  # logistic equation domain\n",
    "\n",
    "# choose optimizer with functional API using functorch\n",
    "optimizer = torchopt.FuncOptimizer(torchopt.adam(lr=learning_rate))\n",
    "\n",
    "# train the model\n",
    "for i in range(num_iter):\n",
    "\n",
    "    # sample colocations points in the domain randomly at each epoch\n",
    "    x = torch.FloatTensor(batch_size).uniform_(domain[0], domain[1])\n",
    "\n",
    "    # update the parameters using the functional API\n",
    "    loss = loss_fn(params, x)\n",
    "    params = optimizer.step(loss, params)\n",
    "\n",
    "    print(f\"Iteration {i} with loss {float(loss)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6095f49",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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