Copy_of_gns_colab_ZK.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jamesterryxu/dsa-2024/blob/main/Copy_of_gns_colab_ZK.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y0EtE29uWUv2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b525ede6-ac47-4774-b548-3a8205e6a33f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "PyTorch has version 2.3.1+cu121 with cuda 12.1\n"
          ]
        }
      ],
      "source": [
        "#Importing Libraries\n",
        "import os\n",
        "import torch\n",
        "import math\n",
        "print(f\"PyTorch has version {torch.__version__} with cuda {torch.version.cuda}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Installing other necessary dependencies\n",
        "!pip install torch_geometric\n",
        "!pip install pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv -f https://data.pyg.org/whl/torch-2.3.0+cu121.html"
      ],
      "metadata": {
        "id": "EGdduR5yDsAO",
        "outputId": "9d797cbf-882d-46af-c5b9-609d755de7f8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "collapsed": true
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: torch_geometric in /usr/local/lib/python3.10/dist-packages (2.5.3)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (4.66.4)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (1.25.2)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (1.11.4)\n",
            "Requirement already satisfied: fsspec in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (2023.6.0)\n",
            "Requirement already satisfied: jinja2 in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (3.1.4)\n",
            "Requirement already satisfied: aiohttp in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (3.9.5)\n",
            "Requirement already satisfied: requests in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (2.31.0)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (3.1.2)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (1.2.2)\n",
            "Requirement already satisfied: psutil>=5.8.0 in /usr/local/lib/python3.10/dist-packages (from torch_geometric) (5.9.5)\n",
            "Requirement already satisfied: aiosignal>=1.1.2 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (1.3.1)\n",
            "Requirement already satisfied: attrs>=17.3.0 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (23.2.0)\n",
            "Requirement already satisfied: frozenlist>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (1.4.1)\n",
            "Requirement already satisfied: multidict<7.0,>=4.5 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (6.0.5)\n",
            "Requirement already satisfied: yarl<2.0,>=1.0 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (1.9.4)\n",
            "Requirement already satisfied: async-timeout<5.0,>=4.0 in /usr/local/lib/python3.10/dist-packages (from aiohttp->torch_geometric) (4.0.3)\n",
            "Requirement already satisfied: MarkupSafe>=2.0 in /usr/local/lib/python3.10/dist-packages (from jinja2->torch_geometric) (2.1.5)\n",
            "Requirement already satisfied: charset-normalizer<4,>=2 in /usr/local/lib/python3.10/dist-packages (from requests->torch_geometric) (3.3.2)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.10/dist-packages (from requests->torch_geometric) (3.7)\n",
            "Requirement already satisfied: urllib3<3,>=1.21.1 in /usr/local/lib/python3.10/dist-packages (from requests->torch_geometric) (2.0.7)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.10/dist-packages (from requests->torch_geometric) (2024.7.4)\n",
            "Requirement already satisfied: joblib>=1.1.1 in /usr/local/lib/python3.10/dist-packages (from scikit-learn->torch_geometric) (1.4.2)\n",
            "Requirement already satisfied: threadpoolctl>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn->torch_geometric) (3.5.0)\n",
            "Looking in links: https://data.pyg.org/whl/torch-2.3.0+cu121.html\n",
            "Requirement already satisfied: pyg_lib in /usr/local/lib/python3.10/dist-packages (0.4.0+pt23cu121)\n",
            "Requirement already satisfied: torch_scatter in /usr/local/lib/python3.10/dist-packages (2.1.2+pt23cu121)\n",
            "Requirement already satisfied: torch_sparse in /usr/local/lib/python3.10/dist-packages (0.6.18+pt23cu121)\n",
            "Requirement already satisfied: torch_cluster in /usr/local/lib/python3.10/dist-packages (1.6.3+pt23cu121)\n",
            "Requirement already satisfied: torch_spline_conv in /usr/local/lib/python3.10/dist-packages (1.2.2+pt23cu121)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from torch_sparse) (1.11.4)\n",
            "Requirement already satisfied: numpy<1.28.0,>=1.21.6 in /usr/local/lib/python3.10/dist-packages (from scipy->torch_sparse) (1.25.2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Importing other needed libraries and packages\n",
        "from torch_geometric.data import Data\n",
        "from torch_geometric.nn import MessagePassing, radius_graph\n",
        "from torch_geometric.utils import add_self_loops\n",
        "import torch_cluster\n",
        "import torch_scatter\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#prints the installed PyTorch version\n",
        "print(f\"PyTorch has version {torch.__version__} with cuda {torch.version.cuda}\")\n",
        "\n",
        "#Making directories to store the train_log and rollouts\n",
        "from torch.utils.tensorboard import SummaryWriter\n",
        "os.makedirs('train_log', exist_ok=True)\n",
        "os.makedirs('rollouts', exist_ok=True)"
      ],
      "metadata": {
        "id": "-sYTZtP6DoL7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f6b787a0-b3eb-439d-c367-cfb39c6594cd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "PyTorch has version 2.3.1+cu121 with cuda 12.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Prints the installed numpy version\n",
        "print(np.__version__)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QrY6KUfsXIIv",
        "outputId": "8dc6eccd-4970-4f64-fdb6-b287f61fb730"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.25.2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# start coding with numpy==1.23.1\n",
        "# !pip uninstall numpy -y\n",
        "# !pip install numpy==1.23.1"
      ],
      "metadata": {
        "id": "I8VjFiaeXU0P"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#importing dependencies\n",
        "import torch.nn as nn\n",
        "from torch.utils.data import Dataset, DataLoader"
      ],
      "metadata": {
        "id": "OTaYxnvVIEid"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#importing dependencies\n",
        "import tree\n",
        "from tqdm import tqdm"
      ],
      "metadata": {
        "id": "EWoR2idfY7bd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#importing dependencies\n",
        "import tensorflow.compat.v1 as tf\n",
        "import tensorflow_datasets as tfds"
      ],
      "metadata": {
        "id": "3N6qVuPkY-zg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "First, create a function to generate a graph from raw data."
      ],
      "metadata": {
        "id": "LSLBKX1KBYxW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#importing dependencies\n",
        "from torch_geometric.data import Data\n",
        "from torch_geometric.nn import radius_graph\n",
        "\n",
        "#A function that generates the graph from raw data (data generated from OpenSeespy)\n",
        "def create_gnn_graph(coordinates, metadata):\n",
        "    \"\"\"\n",
        "    Create a graph data object for a GNN model.\n",
        "\n",
        "    Args:\n",
        "    - coordinates (list of tuples): A list of 2D coordinates for each node.\n",
        "    - E_initial (float): The initial value for the edge attribute.\n",
        "\n",
        "    Returns:\n",
        "    - data (Data): A PyG Data object representing the graph.\n",
        "    \"\"\"\n",
        "\n",
        "    # Convert coordinates to tensor\n",
        "    node_features = torch.tensor(coordinates, dtype=torch.float)\n",
        "\n",
        "    # Add the load as a node attribute\n",
        "    load = torch.rand(node_features.size(0), 1) * metadata[\"P_initial\"]\n",
        "    dist_boundary = torch.norm(node_features - torch.tensor([[0, 0]], dtype=torch.float), dim=1).unsqueeze(1)\n",
        "\n",
        "    # Create edges\n",
        "    num_nodes = len(coordinates)\n",
        "    edge_index = radius_graph(node_features, r=metadata[\"default_connectivity_radius\"], loop=False)\n",
        "\n",
        "    # Calculate edge attributes (e.g., Euclidean distance)\n",
        "    distance = torch.norm(node_features[edge_index[0]] - node_features[edge_index[1]], dim=1).unsqueeze(1)\n",
        "    # Calculate displacement as vector at each edge\n",
        "    displacement = (node_features[edge_index[1]] - node_features[edge_index[0]])\n",
        "\n",
        "    # Convert E_initial to a PyTorch tensor\n",
        "    E_initial = torch.tensor(metadata[\"E_initial\"], dtype=torch.float)\n",
        "    # Correctly generate a tensor with random values uniformly distributed between 0 and 1, then scale by E_initial\n",
        "    E_edge = torch.rand(edge_index.size(1), 1) * E_initial\n",
        "\n",
        "    # Now, both tensors have shape [number_of_edges, 1] and can be concatenated\n",
        "    edge_attr = torch.cat([distance, displacement, E_edge], dim=1)\n",
        "\n",
        "    # Create a graph data object\n",
        "    graph_data = Data(pos=node_features, edge_index=edge_index, edge_attr=edge_attr, node_attr=load)\n",
        "\n",
        "    return graph_data\n",
        "\n",
        "# Example usage\n",
        "metadata = {\"default_connectivity_radius\": 1.6, \"E_initial\": 10, \"P_initial\": 0}\n",
        "coordinates = [(0.5, 0), (1.5, 0), (2.5, 0), (3.5, 0), (4.5, 0)]\n",
        "graph_data = create_gnn_graph(coordinates, metadata)\n",
        "\n",
        "graph = to_networkx(graph_data)\n",
        "nx.draw(graph, with_labels=True)\n",
        "plt.show()\n",
        "\n",
        "print(graph_data.edge_attr)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 659
        },
        "id": "o3j7BB9KBPX3",
        "outputId": "fca22234-9115-400c-d4b3-e7d093a6a7cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ 1.0000, -1.0000,  0.0000,  0.4709],\n",
            "        [ 1.0000,  1.0000,  0.0000,  5.9367],\n",
            "        [ 1.0000, -1.0000,  0.0000,  0.1412],\n",
            "        [ 1.0000,  1.0000,  0.0000,  4.0954],\n",
            "        [ 1.0000, -1.0000,  0.0000,  5.8849],\n",
            "        [ 1.0000,  1.0000,  0.0000,  9.3113],\n",
            "        [ 1.0000, -1.0000,  0.0000,  2.9669],\n",
            "        [ 1.0000,  1.0000,  0.0000,  9.0533]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Check version of cuda\n",
        "import torch\n",
        "print(torch.__version__)\n",
        "print(torch.version.cuda)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Lw_n4CbFDC3C",
        "outputId": "ebb39e5b-6e27-4fd7-b970-bdbe29686d1c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.3.1+cu121\n",
            "12.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "MLP class function"
      ],
      "metadata": {
        "id": "1VM7XVk9Fohd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# class MLP(nn.Module):\n",
        "#     \"\"\"\n",
        "#     Create a simple MLP\n",
        "#     \"\"\"\n",
        "#     def __init__(\n",
        "#         self,\n",
        "#         input_size,\n",
        "#         layer_sizes,\n",
        "#         output_size=None,\n",
        "#         output_activation=torch.nn.Identity,\n",
        "#         activation=torch.nn.ReLU,\n",
        "#         layernorm=True\n",
        "#     ):\n",
        "#         super(MLP, self).__init__()\n",
        "#         sizes = [input_size] + layer_sizes\n",
        "#         if output_size is not None:\n",
        "#             sizes.append(output_size)\n",
        "#         layers = []\n",
        "#         for i in range(len(sizes) - 1):\n",
        "#             layers.append(torch.nn.Linear(sizes[i], sizes[i + 1]))\n",
        "#             if layernorm and i < len(sizes) - 2:\n",
        "#                 layers.append(torch.nn.LayerNorm(sizes[i + 1]))\n",
        "#             if i < len(sizes) - 2:\n",
        "#                 layers.append(activation())\n",
        "#             else:\n",
        "#                 layers.append(output_activation())\n",
        "#         self.model = torch.nn.Sequential(*layers)\n",
        "\n",
        "#     def forward(self, x):\n",
        "#         return self.model(x)"
      ],
      "metadata": {
        "id": "gFMVulxFC9wp"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class MLP(nn.Module):\n",
        "   \"\"\"\n",
        "    Create a simple Multilayer Perceptron (MLP).\n",
        "\n",
        "    Initialize the MLP.\n",
        "\n",
        "    Args:\n",
        "        input_size (int): The size of the input layer.\n",
        "        layer_sizes (list of int): A list of sizes for each hidden layer.\n",
        "        output_size (int, optional): The size of the output layer. If None, there is no specific output layer.\n",
        "        output_activation (torch.nn.Module, optional): The activation function for the output layer. Default is Identity (no activation).\n",
        "        activation (torch.nn.Module, optional): The activation function for the hidden layers. Default is ReLU.\n",
        "\n",
        "    Returns:\n",
        "        None\n",
        "\n",
        "    The `MLP` class creates a feedforward neural network with the specified layers and activations.\n",
        "    It initializes the layers based on the input size, hidden layer sizes, and output size. The forward pass\n",
        "    of the network is defined by the `forward` method, which applies the sequence of linear layers and activations.\n",
        "    \"\"\"\n",
        "    def __init__(\n",
        "        self,\n",
        "        input_size,\n",
        "        layer_sizes,\n",
        "        output_size=None,\n",
        "        output_activation=torch.nn.Identity,\n",
        "        activation=torch.nn.ReLU\n",
        "    ):\n",
        "        super(MLP, self).__init__()\n",
        "        sizes = [input_size] + layer_sizes\n",
        "        if output_size is not None:\n",
        "            sizes.append(output_size)\n",
        "        layers = []\n",
        "        for i in range(len(sizes) - 1):\n",
        "            if (i < len(sizes) - 2):\n",
        "                act = activation\n",
        "            else:\n",
        "                act = output_activation\n",
        "            layers += [torch.nn.Linear(sizes[i], sizes[i + 1]), act()]\n",
        "        self.model = torch.nn.Sequential(*layers)\n",
        "\n",
        "    def forward(self, x):\n",
        "      \"\"\"\n",
        "        Define the forward pass.\n",
        "\n",
        "        Args:\n",
        "        - x (torch.Tensor): The input tensor.\n",
        "\n",
        "        Returns:\n",
        "        - torch.Tensor: The output of the MLP.\n",
        "        \"\"\"\n",
        "        return self.model(x)"
      ],
      "metadata": {
        "id": "FIFg__aOhuyX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Encoder"
      ],
      "metadata": {
        "id": "Vv1aF3njFqhb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Encoder(nn.Module):\n",
        "    def __init__(\n",
        "        self,\n",
        "        node_in, # same shape as the data vertices (nodes) WARNING\n",
        "        node_out, # shape for the processor block\n",
        "        edge_in, # same shape as the data edges (elements)\n",
        "        edge_out, # shape for the processor block\n",
        "        mlp_num_layers,\n",
        "        mlp_hidden_dim,\n",
        "    ):\n",
        "        super(Encoder, self).__init__()\n",
        "\n",
        "        ############################################################################\n",
        "        # TODO: Implement the encoder.\n",
        "        # Hint: The node_fn and edge_fn are of the same structure, which is a MLP layer followed by a layer norm\n",
        "        ############################################################################\n",
        "        self.node_fn = nn.Sequential(*[MLP(node_in, [mlp_hidden_dim for _ in range(mlp_num_layers)], node_out),\n",
        "            nn.LayerNorm(node_out)])\n",
        "        self.edge_fn = nn.Sequential(*[MLP(edge_in, [mlp_hidden_dim for _ in range(mlp_num_layers)], edge_out),\n",
        "            nn.LayerNorm(edge_out)])\n",
        "        ############################################################################\n",
        "\n",
        "    def forward(self, x, e_features): # global_features\n",
        "        '''\n",
        "        Forward pass for the encoder.\n",
        "\n",
        "         x: (E, node_in)\n",
        "        edge_index: (2, E)\n",
        "        e_features: (E, edge_in)\n",
        "\n",
        "        Returns:\n",
        "        - node_out: Tensor of shape (E, node_out) - Transformed node features\n",
        "        - edge_out: Tensor of shape (E, edge_out) - Transformed edge features\n",
        "        '''\n",
        "        return self.node_fn(x), self.edge_fn(e_features)\n",
        "\n",
        "class Decoder(nn.Module):\n",
        "    def __init__(\n",
        "        self,\n",
        "        node_in, # directly from the processor\n",
        "        node_out, # this shape needs to be (num_nodes of real problem x 2). The first column should be u, the second should be p.\n",
        "        edge_in, # directly from the processor\n",
        "        edge_out, # this shape needs to be (num_elements of real problem x 1). The first column should be ei.\n",
        "        mlp_num_layers,\n",
        "        mlp_hidden_dim,\n",
        "    ):\n",
        "        super(Decoder, self).__init__()\n",
        "        ############################################################################\n",
        "        # Implement the decoder.\n",
        "        # The decoder outputs both node and edge information.\n",
        "        ############################################################################\n",
        "        self.node_fn = MLP(node_in, [mlp_hidden_dim for _ in range(mlp_num_layers)], node_out)\n",
        "        self.edge_fn = MLP(edge_in, [mlp_hidden_dim for _ in range(mlp_num_layers)], edge_out)\n",
        "        ############################################################################\n",
        "\n",
        "    def forward(self, x, e_features):\n",
        "       '''\n",
        "        Forward pass for the decoder.\n",
        "\n",
        "        x: Tensor of shape (E, node_in) - Node features\n",
        "        e_features: Tensor of shape (E, edge_in) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - node_out: Tensor of shape (E, node_out) - Decoded node features\n",
        "        - edge_out: Tensor of shape (E, edge_out) - Decoded edge features\n",
        "      '''\n",
        "        ############################################################################\n",
        "        # Implement the forward pass.\n",
        "        ############################################################################\n",
        "        return self.node_fn(x), self.edge_fn(e_features)\n",
        "        ############################################################################\n",
        "\n"
      ],
      "metadata": {
        "id": "iM-Fa5kC_Vtq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sanity check the encoder decoder implementation with the node AND edge outputs"
      ],
      "metadata": {
        "id": "q4_Qn_eRZhX9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Message passing"
      ],
      "metadata": {
        "id": "4qy55GmEF-Hh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class InteractionNetwork(MessagePassing):\n",
        "    # Inherits from pyg.MessagePassing. Much faster!\n",
        "\n",
        "    def __init__(\n",
        "        self,\n",
        "        node_fn, # Function to update node features\n",
        "        edge_fn, # Function to compute messages between nodes\n",
        "    ):\n",
        "        super().__init__()\n",
        "        self.node_fn = node_fn\n",
        "        self.edge_fn = edge_fn\n",
        "\n",
        "    def forward(self, x, edge_index, e_features):\n",
        "      '''\n",
        "        Forward pass of the network.\n",
        "\n",
        "        x: Tensor of shape (N, node_dim) - Node features\n",
        "        edge_index: Tensor of shape (2, E) - Graph connectivity\n",
        "        e_features: Tensor of shape (E, edge_dim) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - x_updated: Tensor of shape (N, updated_node_dim) - Updated node features\n",
        "        - e_updated: Tensor of shape (E, edge_dim) - Updated edge features\n",
        "      '''\n",
        "        x_updated, e_updated = self.propagate(edge_index=edge_index, x=x, e_features=e_features)\n",
        "        return x_updated, e_updated\n",
        "\n",
        "    def message(self, edge_index, x_i, x_j, e_features):\n",
        "      '''\n",
        "        Compute messages sent along the edges.\n",
        "\n",
        "        edge_index: Tensor of shape (2, E) - Graph connectivity\n",
        "        x_i: Tensor of shape (E, node_dim) - Source node features\n",
        "        x_j: Tensor of shape (E, node_dim) - Target node features\n",
        "        e_features: Tensor of shape (E, edge_dim) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - message: Tensor of shape (E, message_dim) - Computed messages\n",
        "        '''\n",
        "        message = torch.cat([x_i, x_j, e_features], dim=-1)\n",
        "        message = self.edge_fn(message)\n",
        "        return message\n",
        "\n",
        "    def aggregate(self, messages, index, dim_size=None):\n",
        "      '''\n",
        "        Aggregate messages from neighboring nodes.\n",
        "\n",
        "        messages: Tensor of shape (E, message_dim) - Computed messages\n",
        "        index: Tensor of shape (E,) - Target node indices for aggregation\n",
        "        dim_size: Optional, size of the dimension for scattering\n",
        "\n",
        "        Returns:\n",
        "        - Tuple (messages, out):\n",
        "            - messages: Tensor of shape (E, message_dim) - Original messages\n",
        "            - out: Tensor of shape (N, message_dim) - Aggregated messages\n",
        "        '''\n",
        "        out = torch_scatter.scatter(messages, index, dim=self.node_dim, dim_size=dim_size, reduce=\"sum\")\n",
        "        return (messages, out)\n",
        "\n",
        "    def update(self, aggr_out, x, e_features):\n",
        "      '''\n",
        "        Update node features using aggregated messages.\n",
        "\n",
        "        aggr_out: Tuple (messages, aggr) - Aggregated messages and original messages\n",
        "        x: Tensor of shape (N, node_dim) - Node features\n",
        "        e_features: Tensor of shape (E, edge_dim) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - x_updated: Tensor of shape (N, updated_node_dim) - Updated node features\n",
        "        - e_updated: Tensor of shape (E, edge_dim) - Updated edge features\n",
        "        '''\n",
        "        message, aggr = aggr_out\n",
        "        x_updated = torch.cat([aggr, x], dim=-1)\n",
        "        x_updated = self.node_fn(x_updated)\n",
        "        return x_updated+x, e_features+message"
      ],
      "metadata": {
        "id": "1s865OW1F9qX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The processer has $M$ layers of InteractionNetworks"
      ],
      "metadata": {
        "id": "ssnOxwogZx73"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Processor(MessagePassing):\n",
        "    def __init__(\n",
        "        self,\n",
        "        node_in, # Input feature dimension for nodes\n",
        "        node_out, # Output feature dimension for nodes\n",
        "        edge_in, # Input feature dimension for edges\n",
        "        edge_out, # Output feature dimension for edges\n",
        "        num_message_passing_steps, # Number of message passing layers\n",
        "        mlp_num_layers, # Number of layers in the MLP\n",
        "        mlp_hidden_dim, # Hidden dimension size for the MLP\n",
        "    ):\n",
        "        super(Processor, self).__init__(aggr='max')\n",
        "        # Define a stack of InteractionNetworks for message passing\n",
        "        self.gnn_stacks = nn.ModuleList([\n",
        "            InteractionNetwork(\n",
        "                node_fn = nn.Sequential(*[MLP(node_in+edge_out, [mlp_hidden_dim for _ in range(mlp_num_layers)], node_out),\n",
        "                nn.LayerNorm(node_out)]),\n",
        "                edge_fn = nn.Sequential(*[MLP(node_in+node_in+edge_in, [mlp_hidden_dim for _ in range(mlp_num_layers)], edge_out),\n",
        "                nn.LayerNorm(edge_out)])\n",
        "            ) for _ in range(num_message_passing_steps)])\n",
        "\n",
        "    def forward(self, x, edge_index, e_features):\n",
        "      '''\n",
        "        Forward pass of the processor.\n",
        "\n",
        "        x: Tensor of shape (N, node_in) - Node features\n",
        "        edge_index: Tensor of shape (2, E) - Graph connectivity\n",
        "        e_features: Tensor of shape (E, edge_in) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - x: Tensor of shape (N, node_out) - Updated node features after message passing\n",
        "        - e_features: Tensor of shape (E, edge_out) - Updated edge features after message passing\n",
        "        '''\n",
        "        for gnn in self.gnn_stacks:\n",
        "            x, e_features = gnn(x, edge_index, e_features)\n",
        "        return x, e_features"
      ],
      "metadata": {
        "id": "8lQlVqBlT8G2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Combining the encoder, processor, and decoder into a single network."
      ],
      "metadata": {
        "id": "6dG5XLWUZ4Wr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class EncodeProcessDecode(nn.Module):\n",
        "    def __init__(\n",
        "        self,\n",
        "        node_in, # Input feature dimension for nodes\n",
        "        node_out, # Output feature dimension for nodes\n",
        "        edge_in, # Input feature dimension for edges\n",
        "        edge_out, # Output feature dimension for edges\n",
        "        latent_dim, # Dimension of latent features\n",
        "        num_message_passing_steps, # Number of message passing layers\n",
        "        mlp_num_layers, # Number of layers in the MLP\n",
        "        mlp_hidden_dim, # Hidden dimension size for the MLP\n",
        "    ):\n",
        "        super(EncodeProcessDecode, self).__init__()\n",
        "        ############################################################################\n",
        "        # Implementation of the encoder, processor, and decoder\n",
        "        ############################################################################\n",
        "        self._encoder = Encoder(\n",
        "            node_in=node_in,\n",
        "            node_out=latent_dim, # Encoder reduces node features to latent_dim\n",
        "            edge_in=edge_in,\n",
        "            edge_out=latent_dim, # Encoder reduces edge features to latent_dim\n",
        "            mlp_num_layers=mlp_num_layers,\n",
        "            mlp_hidden_dim=mlp_hidden_dim,\n",
        "        )\n",
        "\n",
        "        self._processor = Processor(\n",
        "           node_in=latent_dim, # Processor processes latent_dim node features\n",
        "            node_out=latent_dim, # Processor maintains latent_dim node features\n",
        "            edge_in=latent_dim, # Processor processes latent_dim edge features\n",
        "            edge_out=latent_dim, # Processor maintains latent_dim edge features\n",
        "            num_message_passing_steps=num_message_passing_steps,\n",
        "            mlp_num_layers=mlp_num_layers,\n",
        "            mlp_hidden_dim=mlp_hidden_dim,\n",
        "        )\n",
        "\n",
        "        self._decoder = Decoder(\n",
        "            node_in=latent_dim, # Decoder transforms latent_dim node features\n",
        "            node_out=node_out, # Decoder outputs node features of the original dimension\n",
        "            edge_in=latent_dim, # Decoder transforms latent_dim edge features\n",
        "            edge_out=edge_out, # Decoder outputs edge features of the original dimension\n",
        "            mlp_num_layers=mlp_num_layers,\n",
        "            mlp_hidden_dim=mlp_hidden_dim\n",
        "        )\n",
        "        ############################################################################\n",
        "\n",
        "    def forward(self, x, edge_index, e_features):\n",
        "      '''\n",
        "        Forward pass of the architecture.\n",
        "\n",
        "        x: Tensor of shape (E, node_in) - Node features\n",
        "        edge_index: Tensor of shape (2, num_edges) - Graph connectivity\n",
        "        e_features: Tensor of shape (E, edge_in) - Edge features\n",
        "\n",
        "        Returns:\n",
        "        - node_decoded: Tensor of shape (E, node_out) - Decoded node features\n",
        "        - edge_decoded: Tensor of shape (E, edge_out) - Decoded edge features\n",
        "      '''\n",
        "        ############################################################################\n",
        "        # TODO: implementation of making a forward pass through the encoder,\n",
        "        # processor, and decoder blocks\n",
        "        ############################################################################\n",
        "        x, e_features = self._encoder(x, e_features)\n",
        "        x, e_features = self._processor(x, edge_index, e_features)\n",
        "        node_decoded, edge_decoded = self._decoder(x, e_features)\n",
        "        return node_decoded, edge_decoded\n",
        "        ############################################################################\n"
      ],
      "metadata": {
        "id": "nbmwx-L_Z2-Z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The simulator imports the training trajectories. For the static case, it is just a single 1-D array of values that are position, $EI$, $u$, $p$. We put these into the graph."
      ],
      "metadata": {
        "id": "qXSUG_peZ_eB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Simulator(nn.Module):\n",
        "    def __init__(\n",
        "        self,\n",
        "        num_nodes, # Number of nodes in the graph\n",
        "        num_edges, # Number of edges in the graph\n",
        "        node_dimension, # Dimension of the output node features\n",
        "        edge_dimension, # Dimension of the output edge features\n",
        "        node_in, # Dimension of input node features\n",
        "        edge_in, # Dimension of input edge features\n",
        "        latent_dim, # Dimension of latent features for processing\n",
        "        num_message_passing_steps, # Number of message passing steps in the GNN\n",
        "        mlp_num_layers, # Number of layers in the MLP\n",
        "        mlp_hidden_dim, # Hidden dimension size for the MLP\n",
        "        connectivity_radius, # Radius for connectivity in the graph\n",
        "        # device='cpu', # Uncomment if you want to specify a device\n",
        "    ):\n",
        "        super(Simulator, self).__init__()\n",
        "        self._connectivity_radius = connectivity_radius\n",
        "\n",
        "        self._encode_process_decode = EncodeProcessDecode(\n",
        "            node_in=node_in,\n",
        "            node_out=node_dimension, # Dimension of output node features\n",
        "            edge_in=edge_in,\n",
        "            edge_out=edge_dimension, # Dimension of output edge features\n",
        "            latent_dim=latent_dim, # Latent feature dimension\n",
        "            num_message_passing_steps=num_message_passing_steps, # Number of message passing steps\n",
        "            mlp_num_layers=mlp_num_layers, # Number of layers in the MLP\n",
        "            mlp_hidden_dim=mlp_hidden_dim, # Hidden dimension size for the MLP\n",
        "        )\n",
        "\n",
        "        # self._device = device\n",
        "\n",
        "    def forward(self):\n",
        "        pass\n",
        "\n",
        "    def _create_gnn_graph(self, coordinates):\n",
        "        \"\"\"\n",
        "        Create a graph data object for a GNN model.\n",
        "\n",
        "        Args:\n",
        "        - coordinates (list of tuples): A list of 2D coordinates for each node.\n",
        "\n",
        "        Returns:\n",
        "        - data (Data): A PyG Data object representing the graph, with edge and node features purley from the coordinates\n",
        "        \"\"\"\n",
        "\n",
        "        # Convert coordinates to tensor\n",
        "        pos = torch.tensor(coordinates, dtype=torch.float)\n",
        "\n",
        "        # Concat node features and load\n",
        "        node_features = torch.cat([pos], dim=1)\n",
        "        # Create edges\n",
        "        num_nodes = len(coordinates)\n",
        "        edge_index = radius_graph(pos, r=self._connectivity_radius, loop=False)\n",
        "        # Calculate edge attributes (e.g., Euclidean distance)\n",
        "        distance = torch.norm(pos[edge_index[0]] - pos[edge_index[1]], dim=1).unsqueeze(1)\n",
        "        # Calculate displacement as vector at each edge\n",
        "        displacement = (pos[edge_index[1]] - pos[edge_index[0]])\n",
        "\n",
        "        edge_attr = torch.cat([distance, displacement], dim=1)\n",
        "        # Create a graph data object\n",
        "        data = Data(x=node_features, edge_index=edge_index, edge_attr=edge_attr)\n",
        "\n",
        "        return node_features,edge_index, edge_attr\n",
        "\n",
        "    def _decoder_post_processor(self, node_decoded, edge_decoded):\n",
        "      '''\n",
        "        TODO: We want to use the decoded edges and features to feed into the next iteration of gradient step\n",
        "\n",
        "        Post-process the decoded node and edge features.\n",
        "\n",
        "        Args:\n",
        "        - node_decoded: Decoded node features\n",
        "        - edge_decoded: Decoded edge features\n",
        "\n",
        "        Returns:\n",
        "        - u: Node deflections (or other feature, to be defined)\n",
        "      '''\n",
        "      #         edge_decoded = edge_attr = torch.cat([distance, displacement, E_edge], dim=1)\n",
        "      #         node_decoded = node_features = torch.cat([pos, load], dim=1)\n",
        "      # extract the nodal information\n",
        "      u = node_decoded[:,0] # deflection at each node, (num_nodes x 1), one deflection value in meters for each node\n",
        "      # p = node_decoded[:,1] # force applied at each node, (num_nodes x 1), one force magnitude value in meters for each node\n",
        "\n",
        "      # ei = edge_decoded[:,0] # flexural rigidity for each edge, (num_edges x 1), one value for flexural rigidity\n",
        "\n",
        "      return u#,p,ei\n",
        "\n",
        "    def predict_nodes_edges(self, coordinates):\n",
        "      '''\n",
        "        TODO: Change this to predict the new features of u, EI, and p\n",
        "        Predict node and edge features from coordinates.\n",
        "\n",
        "        Args:\n",
        "        - coordinates (list of tuples): A list of 2D coordinates for each node.\n",
        "\n",
        "        Returns:\n",
        "        - u: Predicted node features (e.g., deflections)\n",
        "      '''\n",
        "      node_features, edge_index, e_features = self._create_gnn_graph(coordinates)\n",
        "      node_decoded, edge_decoded = self._encode_process_decode(node_features, edge_index, e_features)\n",
        "      u = self._decoder_post_processor(node_decoded, edge_decoded)\n",
        "\n",
        "      # u,p,ei = self._decoder_post_processor(node_decoded, edge_decoded)\n",
        "      return u#,p,ei  # to be used in loss calculation\n",
        "\n"
      ],
      "metadata": {
        "id": "Hh-PA6PxaL5a"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Coding the training function"
      ],
      "metadata": {
        "id": "qu4-Iynmtu0d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from tqdm import tqdm\n",
        "\n",
        "def train(lr, epoch, simulator, x_data, y_data):\n",
        "    '''\n",
        "    Train the simulator model.\n",
        "\n",
        "    Args:\n",
        "    - lr: Learning rate for the optimizer\n",
        "    - epoch: Number of training epochs\n",
        "    - simulator: The simulator model to be trained\n",
        "    - x_data: Input features for training\n",
        "    - y_data: Target labels for training\n",
        "\n",
        "    Returns:\n",
        "    - train_loss_list: List of tuples containing epoch number and corresponding training loss\n",
        "    - pred_history_list: List of predictions for each epoch\n",
        "    '''\n",
        "  loss_fn = torch.nn.MSELoss() # pure data loss for now\n",
        "  optimizer = torch.optim.Adam(simulator.parameters(), lr=lr)\n",
        "  scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer, gamma=0.1 ** (1 / 5e6))\n",
        "\n",
        "  # recording loss curve\n",
        "  train_loss_list = []\n",
        "  pred_history_list = []\n",
        "  total_step = 0\n",
        "\n",
        "  # first use initial guess of data\n",
        "  data = x_data\n",
        "\n",
        "  for i in range(epoch):\n",
        "\n",
        "    simulator.train() # Set model to training mode\n",
        "    total_loss = 0\n",
        "    batch_count = 0\n",
        "\n",
        "    optimizer.zero_grad() # Clear previous gradients\n",
        "    pred = simulator.predict_nodes_edges(data) # Predict using the simulator\n",
        "    loss_data = loss_fn(pred, y_data) # Compute the loss\n",
        "    loss_data.backward() # Backpropagate the loss\n",
        "    optimizer.step() # Update model parameters\n",
        "    scheduler.step() # Adjust learning rate\n",
        "    print({\"data loss\": loss_data.item(), \"lr\": optimizer.param_groups[0][\"lr\"]}) # Print current loss and learning rate\n",
        "    total_step += 1\n",
        "\n",
        "    # Append current loss and predictions to history\n",
        "    train_loss_list.append((total_step, loss_data.item()))\n",
        "    pred_history_list.append(pred)\n",
        "\n",
        "  return train_loss_list, pred_history_list # return loss and prediction history"
      ],
      "metadata": {
        "id": "9UBjHWyMupqm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "o3l_QDlIwrb4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "11mG-J06wrwj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Time to train"
      ],
      "metadata": {
        "id": "_8VUdp9_wxCa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test out one data set"
      ],
      "metadata": {
        "id": "XobsVrOPeyfE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# load dataset\n",
        "data_df = pd.read_csv(\"node-disp_l=10_n=100_p=1.csv\")\n",
        "\n",
        "# Display the first few rows of the dataframe\n",
        "data_df.head()\n",
        "\n",
        "# Convert the 'position' column to a tensor and reshape it to (100, 1), then cast it to float type\n",
        "data_x = torch.tensor(data_df['position'].values).view(100, 1).float()\n",
        "print(data_x.shape)\n",
        "\n",
        "# Convert the 'displacement' column to a tensor and reshape it to (100, 1), then cast it to float type\n",
        "data_y_np = data_df['displacement'].values\n",
        "data_y = torch.tensor(data_df['displacement']).view(100, 1).float()\n",
        "print(data_y.shape)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WXMp0TwLw5sp",
        "outputId": "70fadfb1-ce5a-4923-ba77-917674161659"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([100, 1])\n",
            "torch.Size([100, 1])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "VQqCYdttgWIN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# build model\n",
        "simulator = Simulator(\n",
        "    num_nodes=100,  # Number of nodes in the graph\n",
        "    num_edges=99,  # Number of edges in the graph (one less than the number of nodes for a linear chain)\n",
        "    node_dimension=1,  # Dimension of node features\n",
        "    edge_dimension=2,  # Dimension of edge features\n",
        "    node_in=1,  # Input dimension for node features\n",
        "    edge_in=2,  # Input dimension for edge features\n",
        "    latent_dim=3,  # Latent dimension for the hidden layers of the model\n",
        "    num_message_passing_steps=2,  # Number of message passing steps in the graph neural network\n",
        "    mlp_num_layers=2,  # Number of layers in the MLP used for node and edge functions\n",
        "    mlp_hidden_dim=3,  # Number of hidden units in each layer of the MLP\n",
        "    connectivity_radius=0.1011,  # Radius for creating edges based on node connectivity\n",
        ")\n"
      ],
      "metadata": {
        "id": "4DTMaPB_b2-X"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ZGW5VuahjKVF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Train the model with specified learning rate, number of epochs, and dataset\n",
        "train_loss_list, pred_history_list = train(lr = 1e-3,\n",
        "      epoch = 1000,\n",
        "      simulator = simulator,\n",
        "      x_data = data_x,\n",
        "      y_data = data_y,\n",
        "      );\n",
        "\n",
        "# The training function returns two lists:\n",
        "# 1. train_loss_list: Contains the loss values recorded during training for each epoch.\n",
        "# 2. pred_history_list: Contains the predictions made by the model during training."
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "collapsed": true,
        "id": "pYkjH1Puf5MD",
        "outputId": "89702501-aa9d-4376-8bca-562391c2c298"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-82-f768a57afd8b>:48: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
            "  pos = torch.tensor(coordinates, dtype=torch.float)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "{'data loss': 5.968330864247751e-12, 'lr': 0.0009995395890030478}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_loss_curves(loss_tuple):\n",
        "  ''' function to plot the loss curve\n",
        "    Args:\n",
        "      loss_tuple: the tuple that comes directly out of the training function\n",
        "  '''\n",
        "  # extract the default tuple\n",
        "  epochs = [item[0] for item in loss_tuple]\n",
        "  loss = [item[1] for item in loss_tuple]\n",
        "  # Creating the plot\n",
        "  fig, ax = plt.subplots(figsize=(10,5))\n",
        "\n",
        "  # Plotting the loss curve\n",
        "  ax.plot(epochs, loss, linestyle='-', alpha=0.25,label='Data loss')\n",
        "\n",
        "  # Adding title and labels\n",
        "  ax.set_title('Loss Curve')\n",
        "  ax.set_xlabel('Epoch')\n",
        "  ax.set_ylabel('Loss')\n",
        "\n",
        "  # Adding a legend\n",
        "  ax.legend()\n",
        "\n",
        "  # Displaying the plot\n",
        "  plt.show()"
      ],
      "metadata": {
        "id": "mDxbvtUVe3NZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "    Plots the training loss curves.\n",
        "\n",
        "    Args:\n",
        "    - loss_tuple: List of tuples where each tuple contains (epoch, loss)\n",
        "    '''\n",
        "plot_loss_curves(loss_tuple=train_loss_list)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "e8iJMbBsnoqC",
        "outputId": "cdc6baed-2359-4744-a579-d15e304f08df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "    Plots the training loss curves.\n",
        "\n",
        "    Args:\n",
        "    - loss_tuple: List of tuples where each tuple contains (epoch, loss)\n",
        "    '''\n",
        "plot_loss_curves(loss_tuple=train_loss_list[0:100])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "xaUuRPC0pz6Z",
        "outputId": "d143f688-f581-48b2-844a-63d8ede84c92"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Convert the tensor to a NumPy array and print it\n",
        "print(pred_history_list[0].cpu().detach().numpy())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K8P3ZJxbqCeK",
        "outputId": "431c64ab-8bd3-4461-906f-137970e86c65"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1.4138222e-04 -3.6567450e-05 -3.6567450e-05 -3.6567450e-05\n",
            " -3.6567450e-05 -3.6567450e-05 -3.6567450e-05 -3.6567450e-05\n",
            " -3.6567450e-05 -3.6567450e-05 -3.6567450e-05 -3.6478043e-05\n",
            " -3.9070845e-05 -4.1037798e-05 -4.2557716e-05 -4.3720007e-05\n",
            " -4.4643879e-05 -4.5359135e-05 -4.5925379e-05 -4.6312809e-05\n",
            " -4.6640635e-05 -4.6968460e-05 -4.7206879e-05 -4.7326088e-05\n",
            " -4.7475100e-05 -4.7564507e-05 -4.7624111e-05 -4.7713518e-05\n",
            " -4.7743320e-05 -4.7802925e-05 -4.7802925e-05 -4.7802925e-05\n",
            " -4.7802925e-05 -4.7802925e-05 -4.7802925e-05 -4.7802925e-05\n",
            " -4.7743320e-05 -4.7713518e-05 -4.7653913e-05 -4.7653913e-05\n",
            " -4.7624111e-05 -4.7624111e-05 -4.7564507e-05 -4.7534704e-05\n",
            " -4.7534704e-05 -4.7415495e-05 -4.7415495e-05 -4.7385693e-05\n",
            " -4.7326088e-05 -4.7296286e-05 -4.7296286e-05 -4.7236681e-05\n",
            " -4.7206879e-05 -4.7206879e-05 -4.7147274e-05 -4.7117472e-05\n",
            " -4.7057867e-05 -4.7028065e-05 -4.6968460e-05 -4.6968460e-05\n",
            " -4.6968460e-05 -4.6968460e-05 -4.6879053e-05 -4.6819448e-05\n",
            " -4.6819448e-05 -4.6789646e-05 -4.6730042e-05 -4.6730042e-05\n",
            " -4.6730042e-05 -4.6640635e-05 -4.6640635e-05 -4.6640635e-05\n",
            " -4.6610832e-05 -4.6610832e-05 -4.6610832e-05 -4.6521425e-05\n",
            " -4.6521425e-05 -4.6432018e-05 -4.6432018e-05 -4.6432018e-05\n",
            " -4.6432018e-05 -4.6372414e-05 -4.6432018e-05 -4.6372414e-05\n",
            " -4.6312809e-05 -4.6283007e-05 -4.6283007e-05 -4.6223402e-05\n",
            " -4.6223402e-05 -4.6193600e-05 -4.6193600e-05 -4.6193600e-05\n",
            " -4.6133995e-05 -4.6133995e-05 -4.6133995e-05 -4.6133995e-05\n",
            " -4.6104193e-05 -4.6044588e-05 -4.6044588e-05  1.3166666e-04]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "print(data_y_np)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "In6x0zwHqOCq",
        "outputId": "660bd2ec-543e-42d3-af4c-2ed7f9c2ea90"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 0.00000e+00 -2.29145e-10 -9.13483e-10 -2.04837e-09 -3.62916e-09\n",
            " -5.65121e-09 -8.10987e-09 -1.10005e-08 -1.43185e-08 -1.80591e-08\n",
            " -2.22178e-08 -2.67898e-08 -3.17706e-08 -3.71555e-08 -4.29399e-08\n",
            " -4.91191e-08 -5.56884e-08 -6.26433e-08 -6.99790e-08 -7.76910e-08\n",
            " -8.57745e-08 -9.42250e-08 -1.03038e-07 -1.12208e-07 -1.21732e-07\n",
            " -1.31603e-07 -1.41819e-07 -1.52374e-07 -1.63263e-07 -1.74481e-07\n",
            " -1.86025e-07 -1.97890e-07 -2.10070e-07 -2.22562e-07 -2.35360e-07\n",
            " -2.48460e-07 -2.61857e-07 -2.75547e-07 -2.89525e-07 -3.03786e-07\n",
            " -3.18326e-07 -3.33140e-07 -3.48223e-07 -3.63571e-07 -3.79179e-07\n",
            " -3.95043e-07 -4.11157e-07 -4.27518e-07 -4.44120e-07 -4.60959e-07\n",
            " -4.78030e-07 -4.95329e-07 -5.12851e-07 -5.30591e-07 -5.48545e-07\n",
            " -5.66708e-07 -5.85075e-07 -6.03642e-07 -6.22404e-07 -6.41356e-07\n",
            " -6.60495e-07 -6.79814e-07 -6.99310e-07 -7.18978e-07 -7.38813e-07\n",
            " -7.58810e-07 -7.78966e-07 -7.99274e-07 -8.19732e-07 -8.40333e-07\n",
            " -8.61074e-07 -8.81949e-07 -9.02955e-07 -9.24086e-07 -9.45337e-07\n",
            " -9.66705e-07 -9.88184e-07 -1.00977e-06 -1.03146e-06 -1.05324e-06\n",
            " -1.07512e-06 -1.09709e-06 -1.11914e-06 -1.14127e-06 -1.16347e-06\n",
            " -1.18575e-06 -1.20809e-06 -1.23048e-06 -1.25294e-06 -1.27545e-06\n",
            " -1.29800e-06 -1.32059e-06 -1.34322e-06 -1.36589e-06 -1.38858e-06\n",
            " -1.41129e-06 -1.43403e-06 -1.45677e-06 -1.47953e-06 -1.50229e-06]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_prediction(prediction, data_y_np, title='Prediction comparison',length=1, num_nodes=100):\n",
        "  ''' function to plot the prediction curve\n",
        "  '''\n",
        "  # Creating the plot\n",
        "  fig, ax = plt.subplots(figsize=(10,5))\n",
        "\n",
        "  beam_length = np.linspace(0, length, num_nodes)\n",
        "\n",
        "  # Plotting the prediction curve\n",
        "  ax.plot(beam_length, prediction, linestyle='-', label='Prediction')\n",
        "  # Plotting true curve\n",
        "  ax.plot(beam_length, data_y_np, linestyle='-', label='True')\n",
        "\n",
        "\n",
        "  # Adding title and labels\n",
        "  ax.set_title('Prediction comparison')\n",
        "  ax.set_xlabel('Length')\n",
        "  ax.set_ylabel('Deflection')\n",
        "\n",
        "  # Adding a legend\n",
        "  ax.legend()\n",
        "\n",
        "  # Displaying the plot\n",
        "  plt.show()"
      ],
      "metadata": {
        "id": "FbCqNKuuqRPx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the predictions from the last entry in pred_history_list compared to the actual data.\n",
        "# - prediction: The predicted values from the final model iteration, converted to a NumPy array.\n",
        "# - data_y_np: The true values to compare against, also as a NumPy array.\n",
        "# - title: Title of the plot to describe what is being shown.\n",
        "# - length: The number of data points to plot. In this case, it is set to 10.\n",
        "plot_prediction(prediction=pred_history_list[-1].cpu().detach().numpy(),\n",
        "                data_y_np=data_y_np,\n",
        "                title='Prediction comparison (only data loss)',\n",
        "                length=10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "u0Y0QZYUrftQ",
        "outputId": "de239353-a0f2-4cdc-909b-ae70eae8f7bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "w3hMXfeXroDc"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}