navier_stokes_equations.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# PINN for Navier-Stokes Equations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "device = 'cuda' if torch.cuda.is_available() else 'cpu'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Brief Overview of Navier-Stokes Equations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The Navier-Stokes equations are a set of partial differential equations that describe the motion of fluid substances. These equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass.\n",
        "\n",
        "Consider an incompressible Newtonian fluid. The two-dimensional Navier-Stokes equations governing the motion of such a fluid are given by:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial u}{\\partial t} + \\lambda_1 \\left( u \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} \\right) = -\\frac{\\partial p}{\\partial x} + \\lambda_2 \\left( \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} \\right)\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\frac{\\partial v}{\\partial t} + \\lambda_1 \\left( u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} \\right) = -\\frac{\\partial p}{\\partial y} + \\lambda_2 \\left( \\frac{\\partial^2 v}{\\partial x^2} + \\frac{\\partial^2 v}{\\partial y^2} \\right)\n",
        "$$\n",
        "\n",
        "where:\n",
        "\n",
        "- $ u(x, y, t) $ and $ v(x, y, t) $ are the *velocity components* of the fluid in the $ x $- and $ y $-directions, respectively, at a given time $ t $.\n",
        "\n",
        "- $ p(x, y, t) $ is the *pressure* field of the fluid at a given point in space and time.\n",
        "\n",
        "- $ \\frac{\\partial u}{\\partial t} $ and $ \\frac{\\partial v}{\\partial t} $ represent the *time derivatives of the velocity components*, $ u $ and $ v $, describing how the velocity evolves over time.\n",
        "\n",
        "- $ \\frac{\\partial u}{\\partial x} $, $ \\frac{\\partial u}{\\partial y} $, $ \\frac{\\partial v}{\\partial x} $, and $ \\frac{\\partial v}{\\partial y} $ are the *spatial derivatives of the velocity components*, representing how the velocity changes in space.\n",
        "\n",
        "- $ \\frac{\\partial p}{\\partial x} $ and $ \\frac{\\partial p}{\\partial y} $ are the *pressure gradients* in the $ x $- and $ y $-directions, respectively, driving fluid motion.\n",
        "\n",
        "- $ \\frac{\\partial^2 u}{\\partial x^2} $, $ \\frac{\\partial^2 u}{\\partial y^2} $, $ \\frac{\\partial^2 v}{\\partial x^2} $, and $ \\frac{\\partial^2 v}{\\partial y^2} $ are the *second-order spatial derivatives of the velocity components*, representing the diffusion (or dissipation) of momentum due to viscosity.\n",
        "\n",
        "- $ \\lambda_1 $ and $ \\lambda_2 $ are constants.\n",
        "\n",
        "Since the fluid is assumed to be incompressible, the continuity equation must be satisfied:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} = 0\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Defining the Model Architecture"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Below, we define the architecture of a model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "class Model(nn.Module):\n",
        "    def __init__(self, hidden_channels:int) -> None:\n",
        "        super().__init__()\n",
        "\n",
        "        self.network = nn.Sequential(\n",
        "            nn.Linear(3, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, hidden_channels),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(hidden_channels, 3)\n",
        "        )\n",
        "\n",
        "    \n",
        "    def forward(self, x:torch.Tensor, y:torch.Tensor, t:torch.Tensor) -> torch.Tensor:\n",
        "        inputs = torch.cat([x, y, t], dim=-1)\n",
        "        output = self.network(inputs)\n",
        "        u, v, p = output[:, 0:1], output[:, 1:2], output[:, 2:3]\n",
        "        return u, v, p"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Infering a System's Parameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "From the Navier Stokes Equations, we can derive two functions, $f$ and $g$ such that:\n",
        "\n",
        "$$\n",
        "f(x, y, t) = \\frac{\\partial u}{\\partial t} + \\lambda_1 \\left( u \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} \\right) + \\frac{\\partial p}{\\partial x} - \\lambda_2 \\left( \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} \\right)\n",
        "$$\n",
        "\n",
        "$$\n",
        "g(x, y, t) = \\frac{\\partial v}{\\partial t} + \\lambda_1 \\left( u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} \\right) + \\frac{\\partial p}{\\partial y} - \\lambda_2 \\left( \\frac{\\partial^2 v}{\\partial x^2} + \\frac{\\partial^2 v}{\\partial y^2} \\right)\n",
        "$$\n",
        "\n",
        "For this task, we want to determine the values of $\\lambda_1$ and $\\lambda_2$. The loss function for this can be represented by the following:\n",
        "\n",
        "$$\n",
        "\\mathcal{L}_{total} = \\mathcal{L}_{physics} + \\mathcal{L}_{data}\n",
        "$$\n",
        "\n",
        "where:\n",
        "- **Physics Loss**\n",
        "$$\n",
        "\\mathcal{L}_{physics} = \\frac{1}{N} \\sum_{i=1}^N \\left(f(x_i, y_i, t_i)^2 + g(x_i, y_i, t_i)^2 \\right)\n",
        "$$\n",
        "\n",
        "- **Data Loss**\n",
        "$$\n",
        "\\mathcal{L}_{data} = \\frac{1}{N} \\sum^{N}_{i} \\left((u(t_i, x_i, y_i) - u_i)^2 + (v(t_i, x_i, y_i) - v_i)^2 \\right)\n",
        "$$\n",
        "\n",
        "We will be importing the dataset used in the [original paper](https://www.sciencedirect.com/science/article/abs/pii/S0021999118307125). In that dataset, the known values of $\\lambda_1$ and $\\lambda_2$ are 1 and 0.01 respectively. Similar to the paper, we will only be training on 1% of the original data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "import scipy\n",
        "\n",
        "data = scipy.io.loadmat('data/cylinder_nektar_wake.mat')\n",
        "\n",
        "U_star = data['U_star']\n",
        "P_star = data['p_star']\n",
        "t_star = data['t']\n",
        "X_star = data['X_star']\n",
        "\n",
        "N = X_star.shape[0]\n",
        "T = t_star.shape[0]\n",
        "\n",
        "x = np.tile(X_star[:,0:1], (1, T)).flatten()[:,None]\n",
        "y = np.tile(X_star[:,1:2], (1, T)).flatten()[:,None]\n",
        "t = np.tile(t_star, (1, N)).T.flatten()[:,None]\n",
        "u = U_star[:,0,:].flatten()[:,None]\n",
        "v = U_star[:,1,:].flatten()[:,None]\n",
        "p = P_star.flatten()[:,None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "idx = np.random.choice(N*T, 5000, replace=False)\n",
        "\n",
        "x = torch.tensor(x[idx,:], dtype=torch.float32).requires_grad_(True).to(device)\n",
        "y = torch.tensor(y[idx,:], dtype=torch.float32).requires_grad_(True).to(device)\n",
        "t = torch.tensor(t[idx,:], dtype=torch.float32).requires_grad_(True).to(device)\n",
        "u = torch.tensor(u[idx,:], dtype=torch.float32).requires_grad_(True).to(device)\n",
        "v = torch.tensor(v[idx,:], dtype=torch.float32).requires_grad_(True).to(device)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "pinn = Model(32).to(device)\n",
        "\n",
        "lambda1 = torch.nn.Parameter(torch.zeros(1, requires_grad=True, device=device))\n",
        "lambda2 = torch.nn.Parameter(torch.zeros(1, requires_grad=True, device=device))\n",
        "\n",
        "optimizer = optim.Adam(list(pinn.parameters()) + [lambda1, lambda2], lr=1e-3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Training Step 1000, Loss: 0.07003951072692871\n",
            "Training Step 2000, Loss: 0.05985632166266441\n",
            "Training Step 3000, Loss: 0.046250030398368835\n",
            "Training Step 4000, Loss: 0.03701475262641907\n",
            "Training Step 5000, Loss: 0.02915847674012184\n",
            "Training Step 6000, Loss: 0.02458089217543602\n",
            "Training Step 7000, Loss: 0.015180250629782677\n",
            "Training Step 8000, Loss: 0.010362713597714901\n",
            "Training Step 9000, Loss: 0.008473003283143044\n",
            "Training Step 10000, Loss: 0.0068975710310041904\n",
            "Training Step 11000, Loss: 0.006975981406867504\n",
            "Training Step 12000, Loss: 0.0045478930696845055\n",
            "Training Step 13000, Loss: 0.004242855589836836\n",
            "Training Step 14000, Loss: 0.0032160114496946335\n",
            "Training Step 15000, Loss: 0.002775282599031925\n",
            "Training Step 16000, Loss: 0.002405458828434348\n",
            "Training Step 17000, Loss: 0.0024254571180790663\n",
            "Training Step 18000, Loss: 0.0024007228203117847\n",
            "Training Step 19000, Loss: 0.0018108610529452562\n",
            "Training Step 20000, Loss: 0.0016145874978974462\n"
          ]
        }
      ],
      "source": [
        "num_training_steps = 20000\n",
        "\n",
        "lambda1_values = []\n",
        "lambda2_values = []\n",
        "\n",
        "for training_step in range(num_training_steps):\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    u_pred, v_pred, p_pred = pinn(x, y, t)\n",
        "\n",
        "    u_x = torch.autograd.grad(u_pred, x, torch.ones_like(u_pred), create_graph=True)[0]\n",
        "    u_y = torch.autograd.grad(u_pred, y, torch.ones_like(u_pred), create_graph=True)[0]\n",
        "    u_t = torch.autograd.grad(u_pred, t, torch.ones_like(u_pred), create_graph=True)[0]\n",
        "\n",
        "    v_x = torch.autograd.grad(v_pred, x, torch.ones_like(v_pred), create_graph=True)[0]\n",
        "    v_y = torch.autograd.grad(v_pred, y, torch.ones_like(v_pred), create_graph=True)[0]\n",
        "    v_t = torch.autograd.grad(v_pred, t, torch.ones_like(v_pred), create_graph=True)[0]\n",
        "\n",
        "    p_x = torch.autograd.grad(p_pred, x, torch.ones_like(p_pred), create_graph=True)[0]\n",
        "    p_y = torch.autograd.grad(p_pred, y, torch.ones_like(p_pred), create_graph=True)[0]\n",
        "\n",
        "    u_xx = torch.autograd.grad(u_x, x, torch.ones_like(u_x), create_graph=True)[0]\n",
        "    u_yy = torch.autograd.grad(u_y, y, torch.ones_like(u_y), create_graph=True)[0]\n",
        "\n",
        "    v_xx = torch.autograd.grad(v_x, x, torch.ones_like(v_x), create_graph=True)[0]\n",
        "    v_yy = torch.autograd.grad(v_y, y, torch.ones_like(v_y), create_graph=True)[0]\n",
        "\n",
        "    # Data Loss\n",
        "    mse_data = torch.mean((u - u_pred)**2 + (v - v_pred)**2)\n",
        "\n",
        "    # Physics Loss\n",
        "    f = u_t + lambda1 * (u_pred * u_x + v_pred * u_y) + p_x - lambda2 * (u_xx + u_yy)\n",
        "    g = v_t + lambda1 * (u_pred * v_x + v_pred * v_y) + p_y - lambda2 * (v_xx + v_yy)\n",
        "\n",
        "    mse_physics = torch.mean(f**2 + g**2)\n",
        "    \n",
        "    # Total Loss\n",
        "    loss = mse_data + mse_physics\n",
        "\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    lambda1_values.append(lambda1.item())\n",
        "    lambda2_values.append(lambda2.item())\n",
        "\n",
        "    if (training_step + 1) % 1000 == 0:\n",
        "        print(f'Training Step {training_step + 1}, Loss: {loss.item()}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let us plot the progression of the values of $\\lambda_1$ and $\\lambda_2$ during training."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
        "\n",
        "# lambda1\n",
        "axes[0].plot(lambda1_values, label=\"Predicted value\")\n",
        "axes[0].hlines(1, 0, len(lambda1_values), label=\"True value\", colors=\"red\")\n",
        "axes[0].set_xlabel(\"Training Step\")\n",
        "axes[0].set_ylabel(\"Value\")\n",
        "axes[0].set_title(\"lambda1\")\n",
        "axes[0].legend()\n",
        "axes[0].grid(True)\n",
        "\n",
        "# Lambda2\n",
        "axes[1].plot(lambda2_values, label=\"Predicted value\")\n",
        "axes[1].hlines(0.01, 0, len(lambda2_values), label=\"True value\", colors=\"red\")\n",
        "axes[1].set_xlabel(\"Training Step\")\n",
        "axes[1].set_ylabel(\"Value\")\n",
        "axes[1].set_title(\"lambda2\")\n",
        "axes[1].legend()\n",
        "axes[1].grid(True)\n",
        "\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": ".venv",
      "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": "3.11.9"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}