notebooks/5_1D_Acoustic_Wave_Source_PINNs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PINNs-Based 1D Acoustic Wave Simulation with a Source Term\n",
    "\n",
    "This notebook presents a neural network aproximation reinforced with PINNs to the solution for the homogeneous 1D elastic wave equation\n",
    "\n",
    "\\begin{equation}\n",
    "\\rho \\partial_t^2 u(x,t) =  \\mu\\partial_x^2 u(x,t) + f(x,t),\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "where:\n",
    "\n",
    "- $ \\rho $ is the constant density of the medium (in kg/m³).\n",
    "- $ u(x,t) $ (in m) is the displacement field, which depends on position $ x $ (in m) and time $ t $ (in s).\n",
    "- $ \\partial_t^2 $ is the second derivative with respect to time, representing acceleration (in 1/s²).\n",
    "- $ \\mu $ is the constant shear modulus, which measures the material's resistance to shear stress (in Pa or N/m² or kg/(m·s²)).\n",
    "- $ \\partial_x^2 $ is the second derivative with respect to position $ x $ (in 1/m²).\n",
    "- $ f(x,t) $ is the external force applied, which depends on position $ x $ (in m) and time $ t $ (in s), and has units of force density (in N/m³ or kg/(m²s²)).\n",
    "\n",
    "\n",
    "In the following code block, we import the necessary libraries for our notebook. This includes NumPy for numerical operations, PyTorch for building and training the neural network, Matplotlib for plotting, a utility module for additional plotting functions, and the time module for timing our training process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries for numerical operations\n",
    "import numpy as np\n",
    "\n",
    "# Import libraries for random operations and data serialization\n",
    "import random\n",
    "import pickle\n",
    "\n",
    "# Import PyTorch libraries for deep learning\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "\n",
    "# Import libraries for data visualization\n",
    "import matplotlib.pyplot as plt\n",
    "from utils_plots import *  # utility module for additional plotting functions\n",
    "\n",
    "# Import libraries for utility functions\n",
    "import time  # to time our training process\n",
    "from scipy.interpolate import griddata  # for data interpolation\n",
    "\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "\n",
    "# Configure warnings\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")  # Ignore warning messages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following code block, we load the data obteined from a spectral elements implemented in the notebook W9_se_homo_1d_solution.ipynb with modified input parameters of the course [computers, waves, simulations](https://www.coursera.org/learn/computers-waves-simulations).\n",
    "\n",
    "The following parameters were chosen for the simulation:\n",
    "\n",
    "- A density ($\\rho$) of 2200 kg/m³.\n",
    "- The shear modulus, denoted by $\\mu$, calculated as the product of density ($\\rho$ = 2200 kg/m³) and the square of the S-wave velocity ($v_{s}$ = 2500 m/s), resulting in 13.75 $\\times 10^{9}$ kg/(m·s²).\n",
    "- The $x$ domain is set to [0, 1000] (m).\n",
    "- The $t$ domain is set to [0, 0.15] (s).\n",
    "\n",
    "The result of the simulation is loaded  in the following cell. Where `t_grid` contain the $t$ domain values, `x_grid` the $x$ domain values and `u_grid` the displacement field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Open the file containing the data\n",
    "with open('traditional_homogeneous_1D/data/4_se_data.pkl', 'rb') as f:\n",
    "    # Load the data from the file\n",
    "    # t_grid, x_grid, and u_grid are expected to be in the file\n",
    "    t_grid, x_grid, u_grid = pickle.load(f)\n",
    "\n",
    "# Convert the loaded data to NumPy arrays for easier manipulation\n",
    "# This step is necessary if the loaded data is not already in NumPy array format\n",
    "x_grid = np.array(x_grid)  # Grid of x values\n",
    "t_grid = np.array(t_grid)  # Grid of t (time) values\n",
    "u_grid = np.array(u_grid)  # Grid of u (wave amplitude) values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This cell generates a new grid of 10,000 points, arranged in a 100x100 matrix, by interpolating the original `x_grid`, `t_grid`, and `u_grid` values using a 'linear' method. In this grid, `x` represents the horizontal axis and `t` represents the vertical axis. This preprocessing of the data is performed to reduce the time required for neural network training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 860x220 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the number of points for the new grid\n",
    "num_points = 101\n",
    "\n",
    "# Create a new grid of points\n",
    "# The range of the grid is determined by the minimum and maximum values of the original grids\n",
    "x_new = np.linspace(np.min(x_grid), np.max(x_grid), num_points)\n",
    "t_new = np.linspace(np.min(t_grid), np.max(t_grid), num_points)\n",
    "\n",
    "# Create a meshgrid using the new x and t values\n",
    "x_grid_new, t_grid_new = np.meshgrid(x_new, t_new)\n",
    "\n",
    "# Prepare the data for interpolation\n",
    "# The original x and t grids are flattened and stacked vertically\n",
    "# The u_grid is also flattened to match the shape\n",
    "points = np.vstack((x_grid.flatten(), t_grid.flatten())).T\n",
    "values = u_grid.flatten()\n",
    "\n",
    "# Perform the interpolation using the 'nearest' method\n",
    "u_grid_new = griddata(points, values, (x_grid_new, t_grid_new), method='nearest')\n",
    "\n",
    "# Identify the NaN values in the interpolated data\n",
    "mask = np.isnan(u_grid_new)\n",
    "\n",
    "# Replace the NaN values with the nearest non-NaN values\n",
    "u_grid_new[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), u_grid_new[~mask])\n",
    "\n",
    "# Update the original grids with the new grids\n",
    "x_grid = x_grid_new\n",
    "t_grid = t_grid_new\n",
    "u_grid = u_grid_new\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(8.6, 2.2))\n",
    "\n",
    "# First subplot\n",
    "contourf_plot=axs[0].contourf(x_grid, t_grid, u_grid, origin='lower', extent=(0, 1, 0, 1), levels=50,cmap='plasma')\n",
    "axs[0].set_xlabel('$x$ (m)')\n",
    "axs[0].set_ylabel('$t$ (s)')\n",
    "axs[0].axhline(np.max(t_grid)/2, color='green')\n",
    "axs[0].axhline(t_grid[-5,0], color='green')\n",
    "fig.colorbar(contourf_plot, ax=axs[0], label='$u$ m')\n",
    "\n",
    "# Second subplot\n",
    "axs[1].plot(x_grid[int(x_grid.shape[0]*0.5),:], u_grid[int(x_grid.shape[0]*0.5),:], color='green', linewidth=2)\n",
    "axs[1].set_xlabel('$x$ (m)')\n",
    "axs[1].set_ylabel('$u$ (m)')\n",
    "axs[1].set_title(\"$t$ (s): {:.2f} s\".format(t_grid[int(x_grid.shape[0]*0.5),0]),fontsize=10)\n",
    "\n",
    "# Third subplot\n",
    "axs[2].plot(x_grid[int(x_grid.shape[0]*0.9),:], u_grid[int(x_grid.shape[0]*0.9),:], color='green', linewidth=2)\n",
    "axs[2].set_xlabel('$x$ (m)')\n",
    "axs[2].set_ylabel('$u$ (m)')\n",
    "axs[2].set_title(\"$t$ (s): {:.2f} s\".format(t_grid[int(x_grid.shape[0]*0.9),0]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This following source function variable for the simulated acoustic wave, creates a grid for the source amplitude, sets the source amplitude at the center of the grid for all time using the defined source function, and then plots a contour graph of the source amplitude over the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x220 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define source parameters\n",
    "f0 = 25.  # Dominant frequency of the source (Hz)\n",
    "t0 = 0.7 / f0  # Source time shift\n",
    "\n",
    "# Define the source function\n",
    "def src(t):\n",
    "    \"\"\"Calculate the source amplitude at a given time.\"\"\"\n",
    "    return -8. * (t - t0) * f0 * (np.exp(-1.0 * (4*f0) ** 2 * (t - t0) ** 2))\n",
    "\n",
    "# Create a grid for the source amplitude\n",
    "# Dimensions are derived from t_grid and x_grid\n",
    "f_grid = np.zeros((len(t_grid[:,0]), len(x_grid[1])))\n",
    "\n",
    "# Set the source amplitude at x=max(x_grid)/2 for all t\n",
    "# Using the defined source function\n",
    "f_grid[:, int(len(x_grid[1])/2)] = src(t_new) \n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(6.0, 2.2))\n",
    "\n",
    "# First subplot\n",
    "contourf_plot=axs[0].contourf(x_grid, t_grid, f_grid, origin='lower', extent=(0, 1, 0, 1), levels=50,cmap='plasma')\n",
    "axs[0].set_xlabel('$x$ (m)')\n",
    "axs[0].set_ylabel('$t$ (s)')\n",
    "#axs[0].axvline(t_grid[:,int(len(x_grid[1])/2)], color='green')\n",
    "fig.colorbar(contourf_plot, ax=axs[0], label='$f(x,t)$ (N/m$^{3}$)')\n",
    "\n",
    "# Second subplot\n",
    "axs[1].plot(t_grid[:,0], f_grid[:,int(len(x_grid[1])/2)], color='green', linewidth=2)\n",
    "axs[1].set_xlabel('$x$ (m)')\n",
    "axs[1].set_ylabel('$f(x,t)$ (N/m$^{3}$)')\n",
    "axs[1].set_title(\"$x$: {:.2f} m\".format(x_grid[0,int(len(x_grid[1])/2)]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable Scaling and Non-Dimensionalization\n",
    "\n",
    "To scale the independent variables ($x$ and $t$) and dependent variables ($u$ and $f$) in equation 1, we need to introduce non-dimensional variables. We denote the characteristic length scale as L (which could be, for instance, the maximum length in the problem), the characteristic time scale as T (such as the maximum time in the problem), and the characteristic displacement and force as $U$ and $F$ respectively.\n",
    "\n",
    "We define the non-dimensional variables as follows:\n",
    "\n",
    "- $ x' = \\frac{x}{L} $\n",
    "\n",
    "- $ t' = \\frac{t}{T} $\n",
    "\n",
    "- $ u' = \\frac{u}{U} $\n",
    "\n",
    "- $ f' = \\frac{f}{F} $\n",
    "\n",
    "Substituting these into the equation 1 yields:\n",
    "\n",
    "\\begin{equation}\\tag{2} \\rho \\frac{U}{T^2} \\frac{\\partial^2 u'}{\\partial {t'}^2} = \\mu \\frac{U}{L^2} \\frac{\\partial^2 u'}{\\partial {x'}^2} + F f'(x',t'). \\end{equation}\n",
    "\n",
    "This results in an equation where all variables have been non-dimensionalized. To simplify, we can define new parameters as follows:\n",
    "\n",
    "- $\\rho' = \\rho \\frac{U}{F T^2}$\n",
    "\n",
    "- $\\mu' = \\mu \\frac{U}{ F L^2}$\n",
    "\n",
    "Substituting these into the equation 2, we get:\n",
    "\n",
    "\\begin{equation}\\tag{3}\n",
    "\\rho'\\frac{\\partial^2 u'}{\\partial {t'}^2} = \\mu' \\frac{\\partial^2 u'}{\\partial {x'}^2} +  f'(x',t').\n",
    "\\end{equation}\n",
    "\n",
    "For the simulation considered in this notebook let's consider:\n",
    "\n",
    "- $\\mu$ = 2500 m/s\n",
    "- $\\rho$ = 2200 kg/m³\n",
    "- U = 9.08 $\\times 10^{-9}$ m\n",
    "- T = 0.15 s\n",
    "- L = 1000 m\n",
    "- F = 0.85 N/m³"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "vs = 2500 # S velocity [m/s] \n",
    "rho = 2200 # Density [kg/m^3]\n",
    "mu = rho * vs**2 # Shear modulus mu\n",
    "U = np.max(u_grid) # max u [m]\n",
    "T = np.max(t_grid) # max t [s]\n",
    "L = np.max(x_grid) # maximun x [m]\n",
    "F = np.max(f_grid) # max f [N/m^3]\n",
    "rho_prime = rho * U / (F*T**2) # [kg/m^2]\n",
    "mu_prime = mu * U / (F*L**2) # [s^2/kg]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following cell we obtain $x'$(`x_prime`), $t'$(`t_prime`), $u'$(`u_prime`) and $f'$(`f_prime`) from $x$(`x_grid`), $y$(`y_grid`), $u$(`u_grid`) and $f$(`f_grid`). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 860x220 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Normalize x_grid by the length L to get dimensionless spatial coordinates\n",
    "x_prime = x_grid / L\n",
    "\n",
    "# Normalize t_grid by the time T to get dimensionless time coordinates\n",
    "t_prime = t_grid / T\n",
    "\n",
    "# Normalize u_grid by the velocity U to get dimensionless velocity\n",
    "u_prime = u_grid / U\n",
    "\n",
    "# Normalize f_grid by the force F to get dimensionless force\n",
    "f_prime = f_grid / F\n",
    "\n",
    "# Limit t_prime_half to the first half of t_prime\n",
    "half_index = t_prime.shape[0] // 2\n",
    "t_prime_half = t_prime[:half_index]\n",
    "\n",
    "# Adjust the other arrays accordingly\n",
    "x_prime_half = x_prime[:half_index]\n",
    "u_prime_half = u_prime[:half_index]\n",
    "f_prime_half = f_prime[:half_index]\n",
    "\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(8.6, 2.2))\n",
    "\n",
    "# First subplot\n",
    "contourf_plot=axs[0].contourf(x_prime, t_prime, u_prime, origin='lower', extent=(0, 1, 0, 1), levels=50,cmap='plasma')\n",
    "axs[0].set_xlabel('$x$ (m)')\n",
    "axs[0].set_ylabel('$t$ (s)')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.5),0], color='green')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.9),0], color='green')\n",
    "fig.colorbar(contourf_plot, ax=axs[0], label='$u$ m')\n",
    "\n",
    "# Second subplot\n",
    "axs[1].plot(x_prime[int(x_prime.shape[0]*0.5),:], u_prime[int(x_prime.shape[0]*0.5),:], color='green', linewidth=2)\n",
    "axs[1].set_xlabel('$x$ (m)')\n",
    "axs[1].set_ylabel('$u$ (m)')\n",
    "axs[1].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.5),0]),fontsize=10)\n",
    "\n",
    "# Third subplot\n",
    "axs[2].plot(x_prime[int(x_prime.shape[0]*0.9),:], u_prime[int(x_prime.shape[0]*0.9),:], color='green', linewidth=2)\n",
    "axs[2].set_xlabel('$x$ (m)')\n",
    "axs[2].set_ylabel('$u$ (m)')\n",
    "axs[2].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.9),0]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x220 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 1, figsize=(3.6, 2.2))\n",
    "\n",
    "# Plot\n",
    "axs.plot(t_prime[:,0], f_prime[:,int(len(x_prime[1])/2)], color='green', linewidth=2)\n",
    "axs.set_xlabel('$t$ (s)')\n",
    "axs.set_ylabel(r'$f(x=0.5 \\text{ m},t)$ (N/m$^{3}$)')\n",
    "axs.set_title(\"$x$: {:.2f} m\".format(x_prime[0,int(len(x_grid[1])/2)]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This cell converts the numpy arrays to PyTorch tensors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert the normalized spatial coordinates to a PyTorch tensor, ensure it's a float, add an extra dimension, and enable gradient computation\n",
    "x_tensor = torch.from_numpy(x_prime).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized time coordinates to a PyTorch tensor, ensure it's a float, add an extra dimension, and enable gradient computation\n",
    "t_tensor = torch.from_numpy(t_prime).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized velocity to a PyTorch tensor, ensure it's a float, and add an extra dimension\n",
    "u_tensor = torch.from_numpy(u_prime).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized force to a PyTorch tensor, ensure it's a float, and add an extra dimension\n",
    "f_tensor = torch.from_numpy(f_prime).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized spatial coordinates to a PyTorch tensor, ensure it's a float, add an extra dimension, and enable gradient computation\n",
    "x_tensor_half = torch.from_numpy(x_prime_half).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized time coordinates to a PyTorch tensor, ensure it's a float, add an extra dimension, and enable gradient computation\n",
    "t_tensor_half = torch.from_numpy(t_prime_half).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized velocity to a PyTorch tensor, ensure it's a float, and add an extra dimension\n",
    "u_tensor_half = torch.from_numpy(u_prime_half).float().unsqueeze(-1).requires_grad_(True)\n",
    "\n",
    "# Convert the normalized force to a PyTorch tensor, ensure it's a float, and add an extra dimension\n",
    "f_tensor_half = torch.from_numpy(f_prime_half).float().unsqueeze(-1).requires_grad_(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This cell defines a neural network with three fully connected layers, creates an instance of this network, and sets up the Adam optimizer and Mean Squared Error loss function for training the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a neural network class with three fully connected layers\n",
    "class NeuralNetwork(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(NeuralNetwork, self).__init__()\n",
    "        # Define the layers\n",
    "        self.layer1 = nn.Linear(2, 10)\n",
    "        self.layer2 = nn.Linear(10, 10)\n",
    "        self.layer3 = nn.Linear(10, 10)\n",
    "        self.output_layer = nn.Linear(10, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        # Define the forward pass\n",
    "        x = torch.tanh(self.layer1(x))\n",
    "        x = torch.tanh(self.layer2(x))\n",
    "        x = torch.tanh(self.layer3(x))\n",
    "        x = self.output_layer(x)\n",
    "        return x\n",
    "\n",
    "# Create an instance of the neural network\n",
    "neural_net = NeuralNetwork()\n",
    "\n",
    "# Define the learning rate\n",
    "learning_rate = 0.0001\n",
    "\n",
    "# Define an optimizer (Adam) for training the network\n",
    "optimizer = optim.Adam(neural_net.parameters(), lr=learning_rate)\n",
    "\n",
    "# Define a loss function (Mean Squared Error) for training the network\n",
    "criterion = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This cell creates the input data by concatenating normalized `x` and `t` grid tensors, defines the output data, and selects a subset for training. The subset consists of the first third of the `t` coordinate and the entire `x` coordinate, chosen using random indices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This cell trains the neural network, tracks the loss over iterations, calculates the training time, and writes a summary of the training process to a text file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 500/100001, MSE: 0.045624060996834984\n",
      "Epoch 1000/100001, MSE: 0.044731052761961994\n",
      "Epoch 1500/100001, MSE: 0.04568046861187037\n",
      "Epoch 2000/100001, MSE: 0.04759427579847108\n",
      "Epoch 2500/100001, MSE: 0.047909952198574406\n",
      "Epoch 3000/100001, MSE: 0.04753498723199565\n",
      "Epoch 3500/100001, MSE: 0.045725755182695976\n",
      "Epoch 4000/100001, MSE: 0.04494287156175563\n",
      "Epoch 4500/100001, MSE: 0.0443497429165043\n",
      "Epoch 5000/100001, MSE: 0.04404084441064119\n",
      "Epoch 5500/100001, MSE: 0.045689591263048314\n",
      "Epoch 6000/100001, MSE: 0.04984123878147664\n",
      "Epoch 6500/100001, MSE: 0.05472487695359405\n",
      "Epoch 7000/100001, MSE: 0.05022231941027309\n",
      "Epoch 7500/100001, MSE: 0.04058608689598194\n",
      "Epoch 8000/100001, MSE: 0.03398409496499752\n",
      "Epoch 8500/100001, MSE: 0.037660956028414204\n",
      "Epoch 9000/100001, MSE: 0.048153162854495245\n",
      "Epoch 9500/100001, MSE: 0.06386748287384961\n",
      "Epoch 10000/100001, MSE: 0.07721753416669899\n",
      "Epoch 10500/100001, MSE: 0.07125559027988837\n",
      "Epoch 11000/100001, MSE: 0.052968644340852335\n",
      "Epoch 11500/100001, MSE: 0.03934095603734807\n",
      "Epoch 12000/100001, MSE: 0.03027887561552898\n",
      "Epoch 12500/100001, MSE: 0.023907042680411134\n",
      "Epoch 13000/100001, MSE: 0.0186320175010951\n",
      "Epoch 13500/100001, MSE: 0.014403849095587387\n",
      "Epoch 14000/100001, MSE: 0.011171632526807057\n",
      "Epoch 14500/100001, MSE: 0.008538783695223675\n",
      "Epoch 15000/100001, MSE: 0.006420576335531141\n",
      "Epoch 15500/100001, MSE: 0.005100303573720625\n",
      "Epoch 16000/100001, MSE: 0.004522020628714632\n",
      "Epoch 16500/100001, MSE: 0.004358541976444886\n",
      "Epoch 17000/100001, MSE: 0.004376344915308933\n",
      "Epoch 17500/100001, MSE: 0.004497371182556623\n",
      "Epoch 18000/100001, MSE: 0.004660182308491264\n",
      "Epoch 18500/100001, MSE: 0.004800895093302174\n",
      "Epoch 19000/100001, MSE: 0.004901265477053682\n",
      "Epoch 19500/100001, MSE: 0.004929992463897297\n",
      "Epoch 20000/100001, MSE: 0.004825231378118746\n",
      "Epoch 20500/100001, MSE: 0.004669898167744584\n",
      "Epoch 21000/100001, MSE: 0.004575816397522027\n",
      "Epoch 21500/100001, MSE: 0.004570002138385402\n",
      "Epoch 22000/100001, MSE: 0.004642813726532628\n",
      "Epoch 22500/100001, MSE: 0.004772943132265875\n",
      "Epoch 23000/100001, MSE: 0.004941077281074042\n",
      "Epoch 23500/100001, MSE: 0.005117864678048187\n",
      "Epoch 24000/100001, MSE: 0.00526846450094512\n",
      "Epoch 24500/100001, MSE: 0.005349908627688682\n",
      "Epoch 25000/100001, MSE: 0.005334422774105893\n",
      "Epoch 25500/100001, MSE: 0.005207922831378608\n",
      "Epoch 26000/100001, MSE: 0.004990006623580257\n",
      "Epoch 26500/100001, MSE: 0.0047126511782304955\n",
      "Epoch 27000/100001, MSE: 0.0044094582926715205\n",
      "Epoch 27500/100001, MSE: 0.004103665180173375\n",
      "Epoch 28000/100001, MSE: 0.0038099536725743973\n",
      "Epoch 28500/100001, MSE: 0.003524497430027506\n",
      "Epoch 29000/100001, MSE: 0.003261264919142419\n",
      "Epoch 29500/100001, MSE: 0.0030164544148664225\n",
      "Epoch 30000/100001, MSE: 0.0027956801396636574\n",
      "Epoch 30500/100001, MSE: 0.0025878892668830104\n",
      "Epoch 31000/100001, MSE: 0.0023972855787976234\n",
      "Epoch 31500/100001, MSE: 0.002223567209137702\n",
      "Epoch 32000/100001, MSE: 0.0020644500294021693\n",
      "Epoch 32500/100001, MSE: 0.0019222610633233338\n",
      "Epoch 33000/100001, MSE: 0.0017984394493287864\n",
      "Epoch 33500/100001, MSE: 0.0016860960666248046\n",
      "Epoch 34000/100001, MSE: 0.001588806059163071\n",
      "Epoch 34500/100001, MSE: 0.0015039518459422693\n",
      "Epoch 35000/100001, MSE: 0.0014322293615411953\n",
      "Epoch 35500/100001, MSE: 0.0013730437914127084\n",
      "Epoch 36000/100001, MSE: 0.0013255974713204585\n",
      "Epoch 36500/100001, MSE: 0.0012874511268344707\n",
      "Epoch 37000/100001, MSE: 0.0012586424102209609\n",
      "Epoch 37500/100001, MSE: 0.0012379518911152542\n",
      "Epoch 38000/100001, MSE: 0.0012245833844884042\n",
      "Epoch 38500/100001, MSE: 0.0012171836839821046\n",
      "Epoch 39000/100001, MSE: 0.0012153809267584444\n",
      "Epoch 39500/100001, MSE: 0.0012180830587876852\n",
      "Epoch 40000/100001, MSE: 0.0012243907426660017\n",
      "Epoch 40500/100001, MSE: 0.0012343506402139482\n",
      "Epoch 41000/100001, MSE: 0.0012468880866844064\n",
      "Epoch 41500/100001, MSE: 0.001262235391762292\n",
      "Epoch 42000/100001, MSE: 0.0012849322257107501\n",
      "Epoch 42500/100001, MSE: 0.0013046291690257512\n",
      "Epoch 43000/100001, MSE: 0.0013276202059923298\n",
      "Epoch 43500/100001, MSE: 0.0013560216072847223\n",
      "Epoch 44000/100001, MSE: 0.0013882067075970028\n",
      "Epoch 44500/100001, MSE: 0.0014199448294516638\n",
      "Epoch 45000/100001, MSE: 0.0014556679169392705\n",
      "Epoch 45500/100001, MSE: 0.0014947753549625765\n",
      "Epoch 46000/100001, MSE: 0.0015372105147946446\n",
      "Epoch 46500/100001, MSE: 0.0015826985339847104\n",
      "Epoch 47000/100001, MSE: 0.0016314806460954777\n",
      "Epoch 47500/100001, MSE: 0.001682057869415851\n",
      "Epoch 48000/100001, MSE: 0.0017405675744097784\n",
      "Epoch 48500/100001, MSE: 0.0017961621731827791\n",
      "Epoch 49000/100001, MSE: 0.0018579743066569373\n",
      "Epoch 49500/100001, MSE: 0.0019215013030844128\n",
      "Epoch 50000/100001, MSE: 0.0019916743220226474\n",
      "Epoch 50500/100001, MSE: 0.0020635341447704787\n",
      "Epoch 51000/100001, MSE: 0.0021376412411719167\n",
      "Epoch 51500/100001, MSE: 0.0022162479085960887\n",
      "Epoch 52000/100001, MSE: 0.0022970392339336583\n",
      "Epoch 52500/100001, MSE: 0.002380619375085705\n",
      "Epoch 53000/100001, MSE: 0.0024666334969334945\n",
      "Epoch 53500/100001, MSE: 0.002555325167821992\n",
      "Epoch 54000/100001, MSE: 0.0026469875556721667\n",
      "Epoch 54500/100001, MSE: 0.002740749163545504\n",
      "Epoch 55000/100001, MSE: 0.0028318021481172715\n",
      "Epoch 55500/100001, MSE: 0.002928405857448731\n",
      "Epoch 56000/100001, MSE: 0.003026096165543413\n",
      "Epoch 56500/100001, MSE: 0.0031253569550186615\n",
      "Epoch 57000/100001, MSE: 0.0032246552034705857\n",
      "Epoch 57500/100001, MSE: 0.003325652068850539\n",
      "Epoch 58000/100001, MSE: 0.003429312489405087\n",
      "Epoch 58500/100001, MSE: 0.0035314050980866834\n",
      "Epoch 59000/100001, MSE: 0.0036353872978786995\n",
      "Epoch 59500/100001, MSE: 0.003739718744141323\n",
      "Epoch 60000/100001, MSE: 0.0038445295848486116\n",
      "Epoch 60500/100001, MSE: 0.00394757618957967\n",
      "Epoch 61000/100001, MSE: 0.004054172934805492\n",
      "Epoch 61500/100001, MSE: 0.004154835808668764\n",
      "Epoch 62000/100001, MSE: 0.004266111216625003\n",
      "Epoch 62500/100001, MSE: 0.0043716027140159475\n",
      "Epoch 63000/100001, MSE: 0.004476001142920579\n",
      "Epoch 63500/100001, MSE: 0.00458194739461641\n",
      "Epoch 64000/100001, MSE: 0.004685726292486831\n",
      "Epoch 64500/100001, MSE: 0.004788959273644376\n",
      "Epoch 65000/100001, MSE: 0.00489440308918345\n",
      "Epoch 65500/100001, MSE: 0.004998206732019602\n",
      "Epoch 66000/100001, MSE: 0.005100324999700754\n",
      "Epoch 66500/100001, MSE: 0.005201689170758151\n",
      "Epoch 67000/100001, MSE: 0.005303626018653935\n",
      "Epoch 67500/100001, MSE: 0.005402491227800915\n",
      "Epoch 68000/100001, MSE: 0.005499743191010549\n",
      "Epoch 68500/100001, MSE: 0.005599120045392642\n",
      "Epoch 69000/100001, MSE: 0.005696163096864068\n",
      "Epoch 69500/100001, MSE: 0.005791801682721705\n",
      "Epoch 70000/100001, MSE: 0.005883124171263608\n",
      "Epoch 70500/100001, MSE: 0.00597354498975536\n",
      "Epoch 71000/100001, MSE: 0.006068699033570965\n",
      "Epoch 71500/100001, MSE: 0.0061553448002649\n",
      "Epoch 72000/100001, MSE: 0.006246458251675185\n",
      "Epoch 72500/100001, MSE: 0.006328167346052797\n",
      "Epoch 73000/100001, MSE: 0.006411015620396954\n",
      "Epoch 73500/100001, MSE: 0.006492194921033566\n",
      "Epoch 74000/100001, MSE: 0.00657244914119553\n",
      "Epoch 74500/100001, MSE: 0.006648670706904886\n",
      "Epoch 75000/100001, MSE: 0.006723184169610214\n",
      "Epoch 75500/100001, MSE: 0.0067945849795169365\n",
      "Epoch 76000/100001, MSE: 0.006866460421275522\n",
      "Epoch 76500/100001, MSE: 0.006935754774590578\n",
      "Epoch 77000/100001, MSE: 0.007002852303643739\n",
      "Epoch 77500/100001, MSE: 0.007068071423538439\n",
      "Epoch 78000/100001, MSE: 0.007130560493526392\n",
      "Epoch 78500/100001, MSE: 0.007191564652250332\n",
      "Epoch 79000/100001, MSE: 0.00725040241482182\n",
      "Epoch 79500/100001, MSE: 0.007307238343838313\n",
      "Epoch 80000/100001, MSE: 0.007362912208474251\n",
      "Epoch 80500/100001, MSE: 0.007416176523699324\n",
      "Epoch 81000/100001, MSE: 0.007469196270458228\n",
      "Epoch 81500/100001, MSE: 0.007524769000574322\n",
      "Epoch 82000/100001, MSE: 0.007568929242077276\n",
      "Epoch 82500/100001, MSE: 0.007619311438057863\n",
      "Epoch 83000/100001, MSE: 0.007662844805211933\n",
      "Epoch 83500/100001, MSE: 0.00770691719220181\n",
      "Epoch 84000/100001, MSE: 0.007752777746784611\n",
      "Epoch 84500/100001, MSE: 0.0077953543764534\n",
      "Epoch 85000/100001, MSE: 0.007836643515076564\n",
      "Epoch 85500/100001, MSE: 0.00787736733083901\n",
      "Epoch 86000/100001, MSE: 0.007916643603717915\n",
      "Epoch 86500/100001, MSE: 0.007956109378909728\n",
      "Epoch 87000/100001, MSE: 0.007992368681861218\n",
      "Epoch 87500/100001, MSE: 0.008028617297661687\n",
      "Epoch 88000/100001, MSE: 0.008064214974146828\n",
      "Epoch 88500/100001, MSE: 0.00809836835577163\n",
      "Epoch 89000/100001, MSE: 0.00813233535540684\n",
      "Epoch 89500/100001, MSE: 0.008165249106371038\n",
      "Epoch 90000/100001, MSE: 0.008197080240738846\n",
      "Epoch 90500/100001, MSE: 0.008229755929526123\n",
      "Epoch 91000/100001, MSE: 0.008260041413031508\n",
      "Epoch 91500/100001, MSE: 0.008291182544065679\n",
      "Epoch 92000/100001, MSE: 0.008319294240891556\n",
      "Epoch 92500/100001, MSE: 0.008348382765746433\n",
      "Epoch 93000/100001, MSE: 0.008376279964092929\n",
      "Epoch 93500/100001, MSE: 0.008403755511284276\n",
      "Epoch 94000/100001, MSE: 0.008430096112322056\n",
      "Epoch 94500/100001, MSE: 0.008456385036213855\n",
      "Epoch 95000/100001, MSE: 0.00848263793309795\n",
      "Epoch 95500/100001, MSE: 0.00850708216325632\n",
      "Epoch 96000/100001, MSE: 0.008531631189162376\n",
      "Epoch 96500/100001, MSE: 0.008555576298616422\n",
      "Epoch 97000/100001, MSE: 0.00857933578237342\n",
      "Epoch 97500/100001, MSE: 0.008602814136543202\n",
      "Epoch 98000/100001, MSE: 0.008625484499733228\n",
      "Epoch 98500/100001, MSE: 0.008647799176783018\n",
      "Epoch 99000/100001, MSE: 0.008669468476002118\n",
      "Epoch 99500/100001, MSE: 0.008691038995070238\n",
      "Epoch 100000/100001, MSE: 0.008711817092526889\n",
      "Finished Training\n"
     ]
    }
   ],
   "source": [
    "inputs_complete = torch.cat((x_tensor, t_tensor), dim=-1)  # x_tensor.shape = torch.Size([201, 201, 1]) and  t_tensor.shape = torch.Size([201, 201, 1])\n",
    "\n",
    "# Assume u_true is the true values\n",
    "u_true = u_prime\n",
    "\n",
    "# Concatenate x and t tensors to form the input data\n",
    "inputs = torch.cat((x_tensor_half, t_tensor_half), dim=-1)  # x_tensor.shape = torch.Size([201, 201, 1]) and  t_tensor.shape = torch.Size([201, 201, 1])\n",
    "\n",
    "# Define the output data\n",
    "outputs = u_tensor_half # u_tensor.shape = torch.Size([201, 201, 1])\n",
    "\n",
    "# Define the dataset\n",
    "dataset = TensorDataset(inputs, outputs)\n",
    "\n",
    "# Define the data loader\n",
    "batch_size = 64\n",
    "data_loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "# Define number of epochs\n",
    "num_epochs = 100_000\n",
    "\n",
    "# List to store losses\n",
    "losses = []\n",
    "mses = []\n",
    "# Training loop\n",
    "for epoch in range(num_epochs):\n",
    "    running_loss = 0.0\n",
    "    for inputs, targets in data_loader:\n",
    "        optimizer.zero_grad()\n",
    "        outputs = neural_net(inputs)\n",
    "        loss = criterion(outputs, targets)\n",
    "        loss.backward(retain_graph=True)\n",
    "        optimizer.step()\n",
    "        running_loss += loss.item()\n",
    "    \n",
    "    epoch_loss = running_loss / len(data_loader)\n",
    "    \n",
    "    # Print loss every 500 epochs\n",
    "    if (epoch + 1) % 500 == 0:\n",
    "        u_pred = neural_net(inputs_complete).detach().numpy().reshape(x_prime.shape)\n",
    "        mse = mean_squared_error(u_true, u_pred)\n",
    "        print(f'Epoch {epoch+1}/{num_epochs}, MSE: {mse}')\n",
    "        losses.append(epoch_loss)\n",
    "        mses.append(mse)\n",
    "print('Finished Training')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an array of iterations\n",
    "iterations = 500*np.arange(len(losses))\n",
    "\n",
    "# Create a figure for the plot\n",
    "fig = plt.figure(figsize=(3.5, 2.5))\n",
    "\n",
    "# Plot the loss values recorded during training\n",
    "plt.semilogy(iterations, losses, color='gray', linewidth=2)\n",
    "\n",
    "# Set the labels for the x and y axes\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Log Loss')\n",
    "\n",
    "# Set the title for the plot\n",
    "plt.title('Training Progress (Log Scale)', fontsize=10)\n",
    "\n",
    "# Display the grid\n",
    "plt.grid(True)\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a figure for the plot\n",
    "fig = plt.figure(figsize=(3.5, 2.5))\n",
    "\n",
    "# Plot the loss values recorded during training\n",
    "plt.semilogy(iterations, mses, color='gray', linewidth=2)\n",
    "\n",
    "# Set the labels for the x and y axes\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Log MSE')\n",
    "\n",
    "# Set the title for the plot\n",
    "plt.title('Training Progress (Log Scale)', fontsize=10)\n",
    "\n",
    "# Display the grid\n",
    "plt.grid(True)\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: MSE = 0.008711867353833136\n"
     ]
    }
   ],
   "source": [
    "# Concatena los tensores x_tensor y t_tensor en una nueva dimensión para crear un tensor de entrada completo\n",
    "inputs_complete = torch.cat((x_tensor, t_tensor), dim=-1)   \n",
    "\n",
    "# Asigna los valores verdaderos de 'u' a la variable u_true\n",
    "u_true = u_prime\n",
    "\n",
    "# Predice los valores de 'u' utilizando la red neuronal, luego los convierte a un array numpy y los reformatea para que tengan la misma forma que x_prime\n",
    "u_pred = neural_net(inputs_complete).detach().numpy().reshape(x_prime.shape)\n",
    "\n",
    "# Calcula el error cuadrático medio (MSE) entre los valores verdaderos y predichos de 'u'\n",
    "mse = mean_squared_error(u_true, u_pred)\n",
    " \n",
    "# Calcula el error absoluto medio (MAE) entre los valores verdaderos y predichos de 'u'\n",
    "mae = mean_absolute_error(u_true, u_pred)\n",
    " \n",
    "# Imprime los valores de MSE y MAE\n",
    "print(f\"Prediction: MSE = {mse}, MAE = {mae}\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NeuralNetwork(\n",
       "  (layer1): Linear(in_features=2, out_features=10, bias=True)\n",
       "  (layer2): Linear(in_features=10, out_features=10, bias=True)\n",
       "  (layer3): Linear(in_features=10, out_features=10, bias=True)\n",
       "  (output_layer): Linear(in_features=10, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Save the trained model's parameters to a file\n",
    "torch.save(neural_net.state_dict(), 'models/5_1D_Wave_Source_PINNs.pth')\n",
    "\n",
    "# Initialize a new instance of the neural network\n",
    "neural_net = NeuralNetwork()\n",
    "\n",
    "# Load the saved parameters into the new instance of the neural network\n",
    "neural_net.load_state_dict(torch.load('models/5_1D_Wave_Source_PINNs.pth'))\n",
    "\n",
    "# Ensure the new neural network is in evaluation mode\n",
    "neural_net.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x200 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Concatenate x and t tensors to form the input data\n",
    "input_data = torch.cat((x_tensor, t_tensor), dim=-1)\n",
    "\n",
    "# Generate predictions using the neural network and reshape to match grid\n",
    "u_pred = neural_net(input_data).detach().numpy().reshape(x_prime.shape)\n",
    "\n",
    "# Rescale u_pred\n",
    "u_pred = u_pred  \n",
    "\n",
    "# Define a function to plot a contour graph\n",
    "def plot_contour(ax, x, t, u, title, label):\n",
    "    im = ax.contourf(x, t, u, origin='lower', levels=50, cmap='plasma', vmin=0, vmax=1) \n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.set_ylabel('$t$')\n",
    "    fig.colorbar(im, ax=ax, label=label)\n",
    "    ax.axhline(y=np.max(t)*0.5, color='yellow')\n",
    "\n",
    "\n",
    "# Create a figure with two subplots\n",
    "fig, axs = plt.subplots(1, 3, figsize=(9, 2))\n",
    "\n",
    "# Plot the original u values\n",
    "plot_contour(axs[0], x_prime, t_prime, u_prime, 'Original', '$u$')\n",
    "\n",
    "# Plot the predicted u values\n",
    "plot_contour(axs[1], x_prime, t_prime, u_pred, 'Predicted', '$u_{pred}$')\n",
    "\n",
    "# Plot the difference between the predicted and analytical u values\n",
    "plot_contour(axs[2], x_prime, t_prime, u_pred-u_prime, 'Difference', '$u_{pred}-u$')\n",
    "\n",
    "# Uncomment the following line to save the plot as a PNG file in the 'imgs' directory\n",
    "fig.savefig('imgs/5_Predicted_and_Difference_1D_Wave_Source_PINNs.png', format='png')\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 860x220 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3, figsize=(8.6, 2.2))\n",
    "\n",
    "# First subplot\n",
    "contourf_plot=axs[0].contourf(x_prime, t_prime, u_pred, origin='lower', extent=(0, 1, 0, 1), levels=50,cmap='plasma', vmin=0, vmax=1)\n",
    "axs[0].set_xlabel('$x$ (m)')\n",
    "axs[0].set_ylabel('$t$ (s)')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.5),0], color='yellow')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.4),0], color='green')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.6),0], color='green')\n",
    "fig.colorbar(contourf_plot, ax=axs[0], label='$u$ m')\n",
    "\n",
    "# Second subplot\n",
    "axs[1].plot(x_prime[int(x_prime.shape[0]*0.4),:], u_pred[int(x_prime.shape[0]*0.4),:], color='green', linewidth=2)\n",
    "axs[1].set_xlabel('$x$ (m)')\n",
    "axs[1].set_ylabel('$u$ (m)')\n",
    "axs[1].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.4),0]),fontsize=10)\n",
    "\n",
    "# Third subplot\n",
    "axs[2].plot(x_prime[int(x_prime.shape[0]*0.9),:], u_pred[int(x_prime.shape[0]*0.9),:], color='green', linewidth=2)\n",
    "axs[2].set_xlabel('$x$ (m)')\n",
    "axs[2].set_ylabel('$u$ (m)')\n",
    "axs[2].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.9),0]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training with Incomplete Data Reinforced using PINNs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a neural network class with three fully connected layers\n",
    "class NeuralNetwork(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(NeuralNetwork, self).__init__()\n",
    "        # Define the layers\n",
    "        self.layer1 = nn.Linear(2, 10)\n",
    "        self.layer2 = nn.Linear(10, 10)\n",
    "        self.layer3 = nn.Linear(10, 10)\n",
    "        self.output_layer = nn.Linear(10, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        # Define the forward pass\n",
    "        x = torch.tanh(self.layer1(x))\n",
    "        x = torch.tanh(self.layer2(x))\n",
    "        x = torch.tanh(self.layer3(x))\n",
    "        x = self.output_layer(x)\n",
    "        return x\n",
    "\n",
    "# Create an instance of the neural network\n",
    "neural_net = NeuralNetwork()\n",
    "\n",
    "# Define the learning rate\n",
    "learning_rate = 0.0001\n",
    "\n",
    "# Define an optimizer (Adam) for training the network\n",
    "optimizer = optim.Adam(neural_net.parameters(), lr=learning_rate)\n",
    "\n",
    "# Define a loss function (Mean Squared Error) for training the network\n",
    "criterion = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 500/100000, Physics Loss: 0.0051451981998980045\n",
      "Epoch 500/100000, Data Loss: 0.036307528614997864\n",
      "Epoch 500/100000, Loss: 0.046705931425094604\n",
      "Epoch 500/100000, MSE: 0.04575343555599523\n",
      "Epoch 1000/100000, Physics Loss: 0.005145200528204441\n",
      "Epoch 1000/100000, Data Loss: 0.036027658730745316\n",
      "Epoch 1000/100000, Loss: 0.04381972551345825\n",
      "Epoch 1000/100000, MSE: 0.046135036855289836\n",
      "Epoch 1500/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 1500/100000, Data Loss: 0.036015406250953674\n",
      "Epoch 1500/100000, Loss: 0.04241335019469261\n",
      "Epoch 1500/100000, MSE: 0.046790754565888916\n",
      "Epoch 2000/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 2000/100000, Data Loss: 0.03602347522974014\n",
      "Epoch 2000/100000, Loss: 0.04186293110251427\n",
      "Epoch 2000/100000, MSE: 0.04733450586377011\n",
      "Epoch 2500/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 2500/100000, Data Loss: 0.03602517768740654\n",
      "Epoch 2500/100000, Loss: 0.04172361269593239\n",
      "Epoch 2500/100000, MSE: 0.04764401444133711\n",
      "Epoch 3000/100000, Physics Loss: 0.005145201459527016\n",
      "Epoch 3000/100000, Data Loss: 0.036003876477479935\n",
      "Epoch 3000/100000, Loss: 0.04168088361620903\n",
      "Epoch 3000/100000, MSE: 0.04773431477246229\n",
      "Epoch 3500/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 3500/100000, Data Loss: 0.03596239164471626\n",
      "Epoch 3500/100000, Loss: 0.04163726419210434\n",
      "Epoch 3500/100000, MSE: 0.0477185184847185\n",
      "Epoch 4000/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 4000/100000, Data Loss: 0.03590282052755356\n",
      "Epoch 4000/100000, Loss: 0.04157833009958267\n",
      "Epoch 4000/100000, MSE: 0.04766569708439754\n",
      "Epoch 4500/100000, Physics Loss: 0.005145200528204441\n",
      "Epoch 4500/100000, Data Loss: 0.03581996262073517\n",
      "Epoch 4500/100000, Loss: 0.04149694740772247\n",
      "Epoch 4500/100000, MSE: 0.04758717403967401\n",
      "Epoch 5000/100000, Physics Loss: 0.005145200993865728\n",
      "Epoch 5000/100000, Data Loss: 0.035702675580978394\n",
      "Epoch 5000/100000, Loss: 0.04138217121362686\n",
      "Epoch 5000/100000, MSE: 0.047471954124679965\n",
      "Epoch 5500/100000, Physics Loss: 0.005145201459527016\n",
      "Epoch 5500/100000, Data Loss: 0.03553184121847153\n",
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      "Epoch 8000/100000, Physics Loss: 0.005145209841430187\n",
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      "Epoch 80000/100000, Physics Loss: 7.872328637859027e-07\n",
      "Epoch 80000/100000, Data Loss: 3.527956869220361e-05\n",
      "Epoch 80000/100000, Loss: 3.629891580203548e-05\n",
      "Epoch 80000/100000, MSE: 0.0023687624927396034\n",
      "Epoch 80500/100000, Physics Loss: 1.0995818229275756e-06\n",
      "Epoch 80500/100000, Data Loss: 3.524255225784145e-05\n",
      "Epoch 80500/100000, Loss: 3.653414023574442e-05\n",
      "Epoch 80500/100000, MSE: 0.002353414897960072\n",
      "Epoch 81000/100000, Physics Loss: 7.366606951109134e-07\n",
      "Epoch 81000/100000, Data Loss: 3.520720565575175e-05\n",
      "Epoch 81000/100000, Loss: 3.613332228269428e-05\n",
      "Epoch 81000/100000, MSE: 0.0023412998062960484\n",
      "Epoch 81500/100000, Physics Loss: 7.33601268620987e-07\n",
      "Epoch 81500/100000, Data Loss: 3.5147892049280927e-05\n",
      "Epoch 81500/100000, Loss: 3.606584868975915e-05\n",
      "Epoch 81500/100000, MSE: 0.0023260068382369636\n",
      "Epoch 82000/100000, Physics Loss: 7.455106469933526e-07\n",
      "Epoch 82000/100000, Data Loss: 3.510404349071905e-05\n",
      "Epoch 82000/100000, Loss: 3.603160075726919e-05\n",
      "Epoch 82000/100000, MSE: 0.002311120710304874\n",
      "Epoch 82500/100000, Physics Loss: 7.243856430250162e-07\n",
      "Epoch 82500/100000, Data Loss: 3.505845961626619e-05\n",
      "Epoch 82500/100000, Loss: 3.5963057598564774e-05\n",
      "Epoch 82500/100000, MSE: 0.0022974260186172965\n",
      "Epoch 83000/100000, Physics Loss: 7.195486091404746e-07\n",
      "Epoch 83000/100000, Data Loss: 3.5017612390220165e-05\n",
      "Epoch 83000/100000, Loss: 3.591355562093668e-05\n",
      "Epoch 83000/100000, MSE: 0.00228413894964514\n",
      "Epoch 83500/100000, Physics Loss: 7.161763733165571e-07\n",
      "Epoch 83500/100000, Data Loss: 3.497148281894624e-05\n",
      "Epoch 83500/100000, Loss: 3.586403181543574e-05\n",
      "Epoch 83500/100000, MSE: 0.0022706257103259943\n",
      "Epoch 84000/100000, Physics Loss: 7.129917776182992e-07\n",
      "Epoch 84000/100000, Data Loss: 3.493244730634615e-05\n",
      "Epoch 84000/100000, Loss: 3.581729106372222e-05\n",
      "Epoch 84000/100000, MSE: 0.0022576250242885777\n",
      "Epoch 84500/100000, Physics Loss: 7.223148941193358e-07\n",
      "Epoch 84500/100000, Data Loss: 3.488679794827476e-05\n",
      "Epoch 84500/100000, Loss: 3.5782413760898635e-05\n",
      "Epoch 84500/100000, MSE: 0.0022450754595233664\n",
      "Epoch 85000/100000, Physics Loss: 7.249731197589426e-07\n",
      "Epoch 85000/100000, Data Loss: 3.484405897324905e-05\n",
      "Epoch 85000/100000, Loss: 3.57420249201823e-05\n",
      "Epoch 85000/100000, MSE: 0.0022318845977747116\n",
      "Epoch 85500/100000, Physics Loss: 9.370510838380142e-07\n",
      "Epoch 85500/100000, Data Loss: 3.4804972528945655e-05\n",
      "Epoch 85500/100000, Loss: 3.5917073546443135e-05\n",
      "Epoch 85500/100000, MSE: 0.002221186260718747\n",
      "Epoch 86000/100000, Physics Loss: 7.953514682412788e-07\n",
      "Epoch 86000/100000, Data Loss: 3.4767570468829945e-05\n",
      "Epoch 86000/100000, Loss: 3.572766945580952e-05\n",
      "Epoch 86000/100000, MSE: 0.0022085575574166154\n",
      "Epoch 86500/100000, Physics Loss: 9.124832445195352e-07\n",
      "Epoch 86500/100000, Data Loss: 3.472889875411056e-05\n",
      "Epoch 86500/100000, Loss: 3.580514021450654e-05\n",
      "Epoch 86500/100000, MSE: 0.002194149700857016\n",
      "Epoch 87000/100000, Physics Loss: 6.976375175327121e-07\n",
      "Epoch 87000/100000, Data Loss: 3.4687571314862e-05\n",
      "Epoch 87000/100000, Loss: 3.554615250322968e-05\n",
      "Epoch 87000/100000, MSE: 0.0021836866433490145\n",
      "Epoch 87500/100000, Physics Loss: 6.89485830207559e-07\n",
      "Epoch 87500/100000, Data Loss: 3.4650522138690576e-05\n",
      "Epoch 87500/100000, Loss: 3.5498109355103225e-05\n",
      "Epoch 87500/100000, MSE: 0.0021724721327214037\n",
      "Epoch 88000/100000, Physics Loss: 7.97285053977248e-07\n",
      "Epoch 88000/100000, Data Loss: 3.4611119190230966e-05\n",
      "Epoch 88000/100000, Loss: 3.557132004061714e-05\n",
      "Epoch 88000/100000, MSE: 0.0021596428494031314\n",
      "Epoch 88500/100000, Physics Loss: 6.829079666204052e-07\n",
      "Epoch 88500/100000, Data Loss: 3.457056300248951e-05\n",
      "Epoch 88500/100000, Loss: 3.54134535882622e-05\n",
      "Epoch 88500/100000, MSE: 0.0021498707672452993\n",
      "Epoch 89000/100000, Physics Loss: 6.815968731643807e-07\n",
      "Epoch 89000/100000, Data Loss: 3.4535616578068584e-05\n",
      "Epoch 89000/100000, Loss: 3.537172233336605e-05\n",
      "Epoch 89000/100000, MSE: 0.0021388264902910555\n",
      "Epoch 89500/100000, Physics Loss: 6.775592851226975e-07\n",
      "Epoch 89500/100000, Data Loss: 3.450017175055109e-05\n",
      "Epoch 89500/100000, Loss: 3.5328772355569527e-05\n",
      "Epoch 89500/100000, MSE: 0.002128375508692603\n",
      "Epoch 90000/100000, Physics Loss: 6.745801215402025e-07\n",
      "Epoch 90000/100000, Data Loss: 3.446334812906571e-05\n",
      "Epoch 90000/100000, Loss: 3.528737215674482e-05\n",
      "Epoch 90000/100000, MSE: 0.002117567905504528\n",
      "Epoch 90500/100000, Physics Loss: 6.735125452905777e-07\n",
      "Epoch 90500/100000, Data Loss: 3.4424800105625764e-05\n",
      "Epoch 90500/100000, Loss: 3.5251345252618194e-05\n",
      "Epoch 90500/100000, MSE: 0.002107308945805496\n",
      "Epoch 91000/100000, Physics Loss: 6.745156611032144e-07\n",
      "Epoch 91000/100000, Data Loss: 3.4391836379654706e-05\n",
      "Epoch 91000/100000, Loss: 3.521329563227482e-05\n",
      "Epoch 91000/100000, MSE: 0.002096257400910828\n",
      "Epoch 91500/100000, Physics Loss: 7.647639677088591e-07\n",
      "Epoch 91500/100000, Data Loss: 3.4360538847977296e-05\n",
      "Epoch 91500/100000, Loss: 3.526886575855315e-05\n",
      "Epoch 91500/100000, MSE: 0.0020860544111161103\n",
      "Epoch 92000/100000, Physics Loss: 6.793699753870897e-07\n",
      "Epoch 92000/100000, Data Loss: 3.432231824262999e-05\n",
      "Epoch 92000/100000, Loss: 3.514533818815835e-05\n",
      "Epoch 92000/100000, MSE: 0.0020764029867078974\n",
      "Epoch 92500/100000, Physics Loss: 6.629877020714048e-07\n",
      "Epoch 92500/100000, Data Loss: 3.428965646889992e-05\n",
      "Epoch 92500/100000, Loss: 3.5093242331640795e-05\n",
      "Epoch 92500/100000, MSE: 0.002066682017739131\n",
      "Epoch 93000/100000, Physics Loss: 6.595940362785768e-07\n",
      "Epoch 93000/100000, Data Loss: 3.425535760470666e-05\n",
      "Epoch 93000/100000, Loss: 3.505468339426443e-05\n",
      "Epoch 93000/100000, MSE: 0.002057026919644171\n",
      "Epoch 93500/100000, Physics Loss: 1.2461686083042878e-06\n",
      "Epoch 93500/100000, Data Loss: 3.423091402510181e-05\n",
      "Epoch 93500/100000, Loss: 3.562877100193873e-05\n",
      "Epoch 93500/100000, MSE: 0.0020444619029371183\n",
      "Epoch 94000/100000, Physics Loss: 6.544238999595109e-07\n",
      "Epoch 94000/100000, Data Loss: 3.418776032049209e-05\n",
      "Epoch 94000/100000, Loss: 3.498137812130153e-05\n",
      "Epoch 94000/100000, MSE: 0.002037460866812214\n",
      "Epoch 94500/100000, Physics Loss: 7.574006986033055e-07\n",
      "Epoch 94500/100000, Data Loss: 3.418380219954997e-05\n",
      "Epoch 94500/100000, Loss: 3.510151873342693e-05\n",
      "Epoch 94500/100000, MSE: 0.002028256342748282\n",
      "Epoch 95000/100000, Physics Loss: 6.548504529746424e-07\n",
      "Epoch 95000/100000, Data Loss: 3.41254890372511e-05\n",
      "Epoch 95000/100000, Loss: 3.491334427963011e-05\n",
      "Epoch 95000/100000, MSE: 0.002018491010405541\n",
      "Epoch 95500/100000, Physics Loss: 6.857124503767409e-07\n",
      "Epoch 95500/100000, Data Loss: 3.409416240174323e-05\n",
      "Epoch 95500/100000, Loss: 3.491146344458684e-05\n",
      "Epoch 95500/100000, MSE: 0.0020102255759512754\n",
      "Epoch 96000/100000, Physics Loss: 6.445640110541717e-07\n",
      "Epoch 96000/100000, Data Loss: 3.406215910217725e-05\n",
      "Epoch 96000/100000, Loss: 3.483662658254616e-05\n",
      "Epoch 96000/100000, MSE: 0.002000652591109135\n",
      "Epoch 96500/100000, Physics Loss: 6.507914349640487e-07\n",
      "Epoch 96500/100000, Data Loss: 3.403079608688131e-05\n",
      "Epoch 96500/100000, Loss: 3.481067324173637e-05\n",
      "Epoch 96500/100000, MSE: 0.001991235530972243\n",
      "Epoch 97000/100000, Physics Loss: 6.44534509319783e-07\n",
      "Epoch 97000/100000, Data Loss: 3.3999804145423695e-05\n",
      "Epoch 97000/100000, Loss: 3.4771997889038175e-05\n",
      "Epoch 97000/100000, MSE: 0.001981822066901082\n",
      "Epoch 97500/100000, Physics Loss: 8.095171324384864e-07\n",
      "Epoch 97500/100000, Data Loss: 3.397699401830323e-05\n",
      "Epoch 97500/100000, Loss: 3.4911125112557784e-05\n",
      "Epoch 97500/100000, MSE: 0.0019727162110477095\n",
      "Epoch 98000/100000, Physics Loss: 6.410831474568113e-07\n",
      "Epoch 98000/100000, Data Loss: 3.393980659893714e-05\n",
      "Epoch 98000/100000, Loss: 3.4749195037875324e-05\n",
      "Epoch 98000/100000, MSE: 0.0019637997456541283\n",
      "Epoch 98500/100000, Physics Loss: 7.641645538569719e-07\n",
      "Epoch 98500/100000, Data Loss: 3.3912678190972656e-05\n",
      "Epoch 98500/100000, Loss: 3.479937367956154e-05\n",
      "Epoch 98500/100000, MSE: 0.0019555640976354543\n",
      "Epoch 99000/100000, Physics Loss: 8.951581094152061e-07\n",
      "Epoch 99000/100000, Data Loss: 3.389673656783998e-05\n",
      "Epoch 99000/100000, Loss: 3.491988900350407e-05\n",
      "Epoch 99000/100000, MSE: 0.001946600560909686\n",
      "Epoch 99500/100000, Physics Loss: 6.298567427620583e-07\n",
      "Epoch 99500/100000, Data Loss: 3.38504250976257e-05\n",
      "Epoch 99500/100000, Loss: 3.460170773905702e-05\n",
      "Epoch 99500/100000, MSE: 0.0019393091224146383\n",
      "Epoch 100000/100000, Physics Loss: 6.274453880905639e-07\n",
      "Epoch 100000/100000, Data Loss: 3.382241993676871e-05\n",
      "Epoch 100000/100000, Loss: 3.456918057054281e-05\n",
      "Epoch 100000/100000, MSE: 0.0019307529851875875\n",
      "Finished Training\n"
     ]
    }
   ],
   "source": [
    "# Concatena los tensores x_tensor y t_tensor para formar el tensor de entrada completo\n",
    "inputs_complete = torch.cat((x_tensor, t_tensor), dim=-1)  \n",
    "\n",
    "# Asume que u_true son los valores verdaderos\n",
    "u_true = u_prime\n",
    "\n",
    "# Concatena los tensores x y t para formar los datos de entrada\n",
    "inputs = torch.cat((x_tensor_half, t_tensor_half), dim=-1)   \n",
    "outputs = u_tensor_half\n",
    "\n",
    "# Selecciona cada 5avo elemento de x_tensor, t_tensor y f_tensor\n",
    "x_tensor_thinned = x_tensor[::5,::5].detach().requires_grad_(True)\n",
    "t_tensor_thinned = t_tensor[::5,::5].detach().requires_grad_(True)\n",
    "f_tensor_thinned = f_tensor[::5,::5].detach().requires_grad_(True)\n",
    "\n",
    "# Concatena los tensores adelgazados\n",
    "inputs_physics= torch.cat((x_tensor_thinned, t_tensor_thinned), dim=-1)\n",
    "\n",
    "# Define el conjunto de datos\n",
    "dataset = TensorDataset(inputs, outputs)\n",
    "\n",
    "# Define el cargador de datos\n",
    "batch_size = 64\n",
    "data_loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "# Define el número de épocas\n",
    "num_epochs = 100_000\n",
    "\n",
    "# Listas para almacenar las pérdidas\n",
    "losses = []\n",
    "mses = []\n",
    "maes = []\n",
    "\n",
    "# Pesos para las pérdidas de física y datos\n",
    "w_d = 1e-0\n",
    "w_p = 1e-0\n",
    "\n",
    "# Define las condiciones iniciales y de frontera\n",
    "u_initial = torch.zeros_like(x_tensor)\n",
    "u_boundary = torch.zeros_like(t_tensor)\n",
    "\n",
    "# Añade las condiciones iniciales y de frontera a las entradas\n",
    "inputs_initial = torch.cat((x_tensor, torch.zeros_like(t_tensor)), dim=-1)\n",
    "inputs_boundary_left = torch.cat((torch.zeros_like(x_tensor), t_tensor), dim=-1)\n",
    "inputs_boundary_right = torch.cat((torch.ones_like(x_tensor), t_tensor), dim=-1)\n",
    "\n",
    "# En el bucle de entrenamiento\n",
    "for epoch in range(num_epochs):\n",
    "    running_loss = 0.0\n",
    "    for inputs, targets in data_loader:\n",
    "        # Pone a cero los gradientes del optimizador\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        # Obtiene las salidas de la red neuronal\n",
    "        outputs = neural_net(inputs)\n",
    "        outputs_ = neural_net(inputs_physics)\n",
    "        \n",
    "        # Calcula la pérdida de los datos\n",
    "        data_loss = criterion(outputs, targets)\n",
    "        \n",
    "        # Calcula las derivadas parciales de las salidas con respecto a x y t\n",
    "        dudx  = torch.autograd.grad(outputs_, x_tensor_thinned, torch.ones_like(outputs_), create_graph=True)[0] # computes du/dx\n",
    "        dudx2 = torch.autograd.grad(dudx,  x_tensor_thinned, torch.ones_like(dudx),  create_graph=True)[0] # computes d^2u/dx^2\n",
    "        dudt  = torch.autograd.grad(outputs_, t_tensor_thinned, torch.ones_like(outputs_), create_graph=True)[0] # computes du/dt\n",
    "        dudt2 = torch.autograd.grad(dudt,  t_tensor_thinned, torch.ones_like(dudt),  create_graph=True)[0] # computes d^2u/dt^2\n",
    "        \n",
    "        # Calcula la pérdida de la física\n",
    "        physics =  rho_prime*dudt2 - mu_prime*dudx2 - f_tensor_thinned \n",
    "        physics_loss = torch.mean(physics**2)        \n",
    "\n",
    "        # Calcula las pérdidas iniciales y de frontera\n",
    "        initial_loss = criterion(neural_net(inputs_initial), u_initial)\n",
    "        boundary_left_loss = criterion(neural_net(inputs_boundary_left), u_boundary)\n",
    "        boundary_right_loss = criterion(neural_net(inputs_boundary_right), u_boundary)\n",
    "    \n",
    "        # Añade las pérdidas iniciales y de frontera a la pérdida total\n",
    "        loss = w_p*physics_loss + w_d*data_loss + initial_loss + boundary_left_loss + boundary_right_loss  \n",
    "\n",
    "        # Realiza la retropropagación y actualiza los pesos\n",
    "        loss.backward(retain_graph=True)\n",
    "        optimizer.step()\n",
    "        \n",
    "        # Acumula la pérdida\n",
    "        running_loss += loss.item()        \n",
    "    \n",
    "    # Calcula la pérdida de la época\n",
    "    epoch_loss = running_loss  \n",
    "     \n",
    "    # Imprime la pérdida cada 500 épocas\n",
    "    if (epoch + 1) % 500 == 0:\n",
    "        u_pred = neural_net(inputs_complete).detach().numpy().reshape(x_prime.shape)\n",
    "        mse = mean_squared_error(u_true, u_pred)\n",
    "        mae = mean_absolute_error(u_true, u_pred)\n",
    "        print(f'Epoch {epoch+1}/{num_epochs}, Physics Loss: {physics_loss}')\n",
    "        print(f'Epoch {epoch+1}/{num_epochs}, Data Loss: {data_loss}')\n",
    "        print(f'Epoch {epoch+1}/{num_epochs}, Loss: {loss}')        \n",
    "        print(f'Epoch {epoch+1}/{num_epochs}, MSE: {mse}')\n",
    "        \n",
    "        # Almacena las pérdidas y errores\n",
    "        losses.append(epoch_loss)\n",
    "        mses.append(mse)\n",
    "        \n",
    "print('Finished Training')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an array of iterations\n",
    "iterations = 500*np.arange(len(losses))\n",
    "\n",
    "# Create a figure for the plot\n",
    "fig = plt.figure(figsize=(3.5, 2.5))\n",
    "\n",
    "# Plot the loss values recorded during training\n",
    "plt.semilogy(iterations, losses, color='gray', linewidth=2)\n",
    "\n",
    "# Set the labels for the x and y axes\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Log Loss')\n",
    "\n",
    "# Set the title for the plot\n",
    "plt.title('Training Progress (Log Scale)', fontsize=10)\n",
    "\n",
    "# Display the grid\n",
    "plt.grid(True)\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an array of iterations\n",
    "iterations = 500*np.arange(len(mses))\n",
    "\n",
    "# Create a figure for the plot\n",
    "fig = plt.figure(figsize=(3.5, 2.5))\n",
    "\n",
    "# Plot the loss values recorded during training\n",
    "plt.semilogy(iterations,mses, color='gray', linewidth=2)\n",
    "\n",
    "# Set the labels for the x and y axes\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Log MSE')\n",
    "\n",
    "# Set the title for the plot\n",
    "plt.title('Training Progress (Log Scale)', fontsize=10)\n",
    "\n",
    "# Display the grid\n",
    "plt.grid(True)\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction: MSE = 0.0019307529851875875, MAE = 0.01652064332304503\n"
     ]
    }
   ],
   "source": [
    "# Concatena los tensores x_tensor y t_tensor para formar los datos de entrada\n",
    "# x_tensor y t_tensor tienen la misma forma: torch.Size([201, 201, 1])\n",
    "inputs = torch.cat((x_tensor, t_tensor), dim=-1)  \n",
    "\n",
    "# Usa la red neuronal para predecir los valores de 'u' basándose en los datos de entrada\n",
    "# Después, se desacopla el tensor resultante, se convierte a numpy y se redimensiona a la forma de x_prime\n",
    "u_pred = neural_net(inputs).detach().numpy().reshape(x_prime.shape)\n",
    "\n",
    "# Asume que u_true son los valores verdaderos\n",
    "u_true = u_prime\n",
    "\n",
    "# Calcula el error cuadrático medio (MSE) entre los valores verdaderos y las predicciones\n",
    "mse = mean_squared_error(u_true, u_pred)\n",
    " \n",
    "# Calcula el error absoluto medio (MAE) entre los valores verdaderos y las predicciones\n",
    "mae = mean_absolute_error(u_true, u_pred)\n",
    " \n",
    "# Imprime los errores calculados\n",
    "print(f\"Prediction: MSE = {mse}, MAE = {mae}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x200 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Concatenate x and t tensors to form the input data\n",
    "input_data = torch.cat((x_tensor, t_tensor), dim=-1)\n",
    "# Generate predictions using the neural network and reshape to match grid\n",
    "u_pred = neural_net(input_data).detach().numpy().reshape(x_prime.shape)\n",
    "\n",
    "# Rescale u_pred\n",
    "u_pred = u_pred #* np.max(u_prime)  \n",
    "\n",
    "# Define a function to plot a contour graph\n",
    "def plot_contour(ax, x, t, u, title, label):\n",
    "    im = ax.contourf(x, t, u, origin='lower', levels=50, cmap='plasma', vmin=0, vmax=1) \n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.set_ylabel('$t$')\n",
    "    fig.colorbar(im, ax=ax, label=label)\n",
    "    ax.axhline(y=np.max(t)*0.5, color='yellow')\n",
    "\n",
    "\n",
    "# Create a figure with two subplots\n",
    "fig, axs = plt.subplots(1, 3, figsize=(9, 2))\n",
    "\n",
    "# Plot the original u values\n",
    "plot_contour(axs[0], x_prime, t_prime, u_prime, 'Original', '$u$')\n",
    "\n",
    "# Plot the predicted u values\n",
    "plot_contour(axs[1], x_prime, t_prime, u_pred, 'Predicted', '$u_{pred}$')\n",
    "\n",
    "# Plot the difference between the predicted and analytical u values\n",
    "plot_contour(axs[2], x_prime, t_prime, u_pred-u_prime, 'Difference', '$u_{pred}-u$')\n",
    "\n",
    "# Uncomment the following line to save the plot as a PNG file in the 'imgs' directory\n",
    "fig.savefig('imgs/5_Predicted_and_Difference_1D_Wave_Source_PINNs.png', format='png')\n",
    "\n",
    "# Display the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 860x220 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3, figsize=(8.6, 2.2))\n",
    "\n",
    "# First subplot\n",
    "contourf_plot=axs[0].contourf(x_prime, t_prime, u_pred, origin='lower', extent=(0, 1, 0, 1), levels=50,cmap='plasma', vmin=0, vmax=1)\n",
    "axs[0].set_xlabel('$x$ (m)')\n",
    "axs[0].set_ylabel('$t$ (s)')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.5),0], color='yellow')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.4),0], color='green')\n",
    "axs[0].axhline(t_prime[int(x_prime.shape[0]*0.6),0], color='green')\n",
    "fig.colorbar(contourf_plot, ax=axs[0], label='$u$ m')\n",
    "\n",
    "# Second subplot\n",
    "axs[1].plot(x_prime[int(x_prime.shape[0]*0.4),:], u_pred[int(x_prime.shape[0]*0.4),:], color='green', linewidth=2)\n",
    "axs[1].set_xlabel('$x$ (m)')\n",
    "axs[1].set_ylabel('$u$ (m)')\n",
    "axs[1].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.4),0]),fontsize=10)\n",
    "\n",
    "# Third subplot\n",
    "axs[2].plot(x_prime[int(x_prime.shape[0]*0.9),:], u_pred[int(x_prime.shape[0]*0.9),:], color='green', linewidth=2)\n",
    "axs[2].set_xlabel('$x$ (m)')\n",
    "axs[2].set_ylabel('$u$ (m)')\n",
    "axs[2].set_title(\"$t$ (s): {:.2f} s\".format(t_prime[int(x_prime.shape[0]*0.9),0]),fontsize=10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NeuralNetwork(\n",
       "  (layer1): Linear(in_features=2, out_features=10, bias=True)\n",
       "  (layer2): Linear(in_features=10, out_features=10, bias=True)\n",
       "  (layer3): Linear(in_features=10, out_features=10, bias=True)\n",
       "  (output_layer): Linear(in_features=10, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Save the trained model's parameters to a file\n",
    "torch.save(neural_net.state_dict(), 'models/5_1D_Wave_Source_PINNs_Reinforced.pth')\n",
    "\n",
    "# Initialize a new instance of the neural network\n",
    "neural_net = NeuralNetwork()\n",
    "\n",
    "# Load the saved parameters into the new instance of the neural network\n",
    "neural_net.load_state_dict(torch.load('models/5_1D_Wave_Source_PINNs_Reinforced.pth'))\n",
    "\n",
    "# Ensure the new neural network is in evaluation mode\n",
    "neural_net.eval()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pinn",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}