avivajpeyi/hacking_with_kate.ipynb

## hacking_with_kate.ipynb
{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/avivajpeyi/e2a0fe98ce53eebc610e9cec6f59fd0d/hacking_with_kate.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Flows with a NN\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "8XaG_TTjm5ba"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "id": "lIYdn1woOS1n"
      },
      "outputs": [],
      "source": [
        "from tqdm.auto import tqdm, trange\n",
        "import matplotlib\n",
        "import shutil\n",
        "import os\n",
        "import numpy as np\n",
        "from tensorflow import keras\n",
        "import matplotlib.pyplot as plt\n",
        "import imageio\n",
        "import re\n",
        "import glob\n",
        "\n",
        "# Clear all previously registered custom objects\n",
        "keras.saving.get_custom_objects().clear()\n",
        "\n",
        "\n",
        "def generate_time_samples(N):\n",
        "    t = np.random.uniform(0, 1, N)\n",
        "    return t\n",
        "\n",
        "\n",
        "def generate_path_samples(X_1, t, sigma_min):\n",
        "    n, dim = X_1.shape\n",
        "    mu_t = np.multiply(X_1, t.reshape(-1, 1))\n",
        "    sigma_t = 1 - (1 - sigma_min) * t\n",
        "    X_t = np.random.multivariate_normal(np.zeros(dim), np.diag(np.ones(dim)), n)\n",
        "    X_t = np.multiply(X_t, sigma_t.reshape(-1, 1)) + mu_t\n",
        "    return X_t\n",
        "\n",
        "\n",
        "def find_u_path(X_1, X_t, t, sigma_min):\n",
        "    numerator = X_1 - (1 - sigma_min) * X_t\n",
        "    denom = 1 - (1 - sigma_min) * t\n",
        "    u_t = np.divide(numerator.T, denom.T).T\n",
        "    return u_t\n",
        "\n",
        "\n",
        "@keras.saving.register_keras_serializable(package=\"my_package\", name=\"custom_loss\")\n",
        "def custom_loss(y_true, y_pred):\n",
        "    return keras.losses.mean_squared_error(y_true, y_pred)\n",
        "\n",
        "\n",
        "def build_and_train_model(\n",
        "    X_t, t, u_t, epochs=50, batch_size=32, fname=\"basic_nn.keras\"\n",
        "):\n",
        "    n, dim = X_t.shape\n",
        "    model = keras.Sequential(\n",
        "        [\n",
        "            keras.layers.Input(shape=(dim + 1,)),  # Input layer for (X_t, t)\n",
        "            keras.layers.Dense(64, activation=\"relu\"),\n",
        "            keras.layers.Dense(32, activation=\"relu\"),\n",
        "            keras.layers.Dense(dim),  # Output layer for u_t\n",
        "        ]\n",
        "    )\n",
        "\n",
        "    # Compile the model\n",
        "    model.compile(optimizer=\"adam\", loss=custom_loss)\n",
        "\n",
        "    # Initialize lists to store training history\n",
        "    loss_history = []\n",
        "\n",
        "    # Create a tqdm progress bar\n",
        "    progress_bar = tqdm(total=epochs, desc=\"Training Progress\")\n",
        "\n",
        "    # Train the model using (X_t, t) as input and u_t as output\n",
        "    for epoch in range(epochs):\n",
        "        history = model.fit(\n",
        "            np.column_stack((X_t, t)), u_t, batch_size=batch_size, verbose=0\n",
        "        )\n",
        "        loss = history.history[\"loss\"][0]\n",
        "        loss_history.append(loss)\n",
        "        progress_bar.update(1)  # Update the progress bar\n",
        "        progress_bar.set_postfix({\"Loss\": loss})  # Update progress bar description\n",
        "\n",
        "    progress_bar.close()  # Close the progress bar\n",
        "\n",
        "    # Plot the training loss over epochs\n",
        "    plt.plot(range(1, epochs + 1), loss_history)\n",
        "    plt.xlabel(\"Epochs\")\n",
        "    plt.ylabel(\"Loss\")\n",
        "    plt.title(\"Training Loss Progress\")\n",
        "    plt.show()\n",
        "\n",
        "    model.save(fname)\n",
        "    return model\n",
        "\n",
        "\n",
        "def model_generator(X_1, fname=\"basic_nn.keras\", epochs=50):\n",
        "    # Step 1: generateproposal distribution\n",
        "    N, ndim = X_1.shape\n",
        "    X_0 = np.random.multivariate_normal(np.zeros(ndim), np.diag(np.ones(ndim)), N)\n",
        "\n",
        "    # Step 2: Generate N-samples for time, t ~ U[0, 1]\n",
        "    t = generate_time_samples(N)\n",
        "\n",
        "    # Step 3: Generate N-samples in the path using X_1 and t\n",
        "    sigma_min = 0.1\n",
        "    X_t = generate_path_samples(X_1, t, sigma_min)\n",
        "\n",
        "    # Step 4: Find u-path\n",
        "    u_t = find_u_path(X_1, X_t, t, sigma_min)\n",
        "\n",
        "    # Step 5: Build and train the DNN model\n",
        "    model = build_and_train_model(X_t, t, u_t, fname=fname, epochs=epochs)\n",
        "    return model\n",
        "\n",
        "\n",
        "def make_gif(image_re, fname=\"tmp.gif\", duration=0.1, true_image=False):\n",
        "    images = glob.glob(image_re)\n",
        "    # sort by int\n",
        "    images = sorted(images, key=lambda x: int(re.findall(r\"\\d+\", x)[-1]))\n",
        "    images = [imageio.v3.imread(fname) for fname in images]\n",
        "    # also add in reverse to help loop\n",
        "    images += images[::-1]\n",
        "    imageio.mimsave(fname, images, duration=duration, loop=0)\n",
        "    return fname\n",
        "\n",
        "\n",
        "def generate_flow_data(X_0, t, model):\n",
        "    nparticles, ndim = X_0.shape\n",
        "    X_i = X_0\n",
        "    dt = t[1] - t[0]\n",
        "    X_vals = np.zeros((len(t), nparticles, ndim))\n",
        "    X_vals[0] = X_0\n",
        "    for i in trange(1, len(t), desc=\"Generating flow data\"):\n",
        "        data = np.column_stack((X_i, np.ones(nparticles) * t[i]))\n",
        "        # predict without any logging\n",
        "        u_t = model.predict(data, verbose=0)\n",
        "        X_i = X_i + u_t * dt\n",
        "        X_vals[i, :] = X_i\n",
        "    return X_vals\n",
        "\n",
        "\n",
        "def plot_flow_gif(X_vals, outdir=\"tmp\"):\n",
        "    if os.path.exists(outdir):\n",
        "        shutil.rmtree(outdir)\n",
        "    os.makedirs(outdir, exist_ok=True)\n",
        "    N = len(X_vals)\n",
        "\n",
        "    init_data = X_vals[0]\n",
        "    final_data = X_vals[N - 1]\n",
        "\n",
        "    colormap = matplotlib.colormaps[\"summer\"]\n",
        "    for i in trange(N, desc=\"Making gif\"):\n",
        "        fig, ax = plt.subplots(1, 1)\n",
        "        # make background black\n",
        "        ax.set_facecolor(\"black\")\n",
        "        ax.set_xlabel(\"X\")\n",
        "        ax.set_ylabel(\"Y\")\n",
        "        ax.set_title(f\"Flow of Particles {int(100 * i / N)}%\")\n",
        "        ax.plot(X_vals[i][:, 0], X_vals[i][:, 1], \".\", alpha=0.8, color=colormap(i / N))\n",
        "        # scatter plot for initial and final data, using the final colors\n",
        "        ax.plot(\n",
        "            init_data[:, 0],\n",
        "            init_data[:, 1],\n",
        "            \".\",\n",
        "            color=colormap(0),\n",
        "            alpha=0.3,\n",
        "            zorder=-1,\n",
        "        )\n",
        "        ax.plot(\n",
        "            final_data[:, 0],\n",
        "            final_data[:, 1],\n",
        "            \".\",\n",
        "            color=colormap(N - 1 / N),\n",
        "            alpha=0.3,\n",
        "            zorder=-1,\n",
        "        )\n",
        "        plt.savefig(f\"{outdir}/tmp{i:003}.png\")\n",
        "        plt.close()\n",
        "\n",
        "    make_gif(f\"{outdir}/tmp*.png\", fname=f\"{outdir}/flow.gif\", duration=0.1)\n",
        "\n",
        "\n",
        "def main(X_1, n_tvals=10, n_particles=100, outdir=\"tmp\", epochs=50):\n",
        "    model = model_generator(X_1, epochs=epochs)\n",
        "    X_0 = np.random.multivariate_normal([0, 0], np.diag([0.2, 0.2]), n_particles)\n",
        "    t = np.linspace(0, 1, n_tvals)\n",
        "    X_vals = generate_flow_data(X_0, t, model)\n",
        "    plot_flow_gif(X_vals, outdir)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "## 1 Gaussian\n",
        "X_1 = np.random.multivariate_normal([4, -5], np.diag([0.5, 2]), 200)\n",
        "main(X_1, n_tvals=50, n_particles=10000, outdir=\"1gaussian\")\n",
        "\n"
      ],
      "metadata": {
        "id": "3IP0M_u1NBRo",
        "outputId": "019882ce-4641-4836-b02e-adacc991ce37",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 568,
          "referenced_widgets": [
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      },
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Training Progress:   0%|          | 0/20 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "6c1ba607ed0d4dbb8cf9f2526271c1c8"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Generating flow data:   0%|          | 0/49 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "ca300f98c4734e309215a9dc360e7656"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Making gif:   0%|          | 0/50 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "db060ff2f905408f94b23601bd605ba3"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "![1G](https://user-images.githubusercontent.com/15642823/266222217-3bc950eb-6daf-49c3-ab35-7f124998997e.gif)"
      ],
      "metadata": {
        "id": "gD3W6XKsTVTe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## 4 Gaussians\n",
        "X_1 = np.concatenate(\n",
        "    [\n",
        "        np.random.multivariate_normal([0, 3], np.diag([0.5, 0.5]), 300),\n",
        "        np.random.multivariate_normal([0, -3], np.diag([0.5, 0.5]), 300),\n",
        "        np.random.multivariate_normal([-3, 0], np.diag([0.5, 0.5]), 300),\n",
        "        np.random.multivariate_normal([3, 0], np.diag([0.5, 0.5]), 300),\n",
        "    ]\n",
        ")\n",
        "main(X_1, n_tvals=50, n_particles=10000, outdir=\"4gaussian\")\n"
      ],
      "metadata": {
        "id": "BwvNu98kRDdY",
        "outputId": "845b8919-18c5-483b-a7d6-16b37cd52666",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 568,
          "referenced_widgets": [
            "93efb70d726a4d98b69a9fa610a23cf7",
            "846a39c1ea63476c99b08b2ad6d9c1b2",
            "2c60b29cc01049cd97df5875bed984a7",
            "ba2d8655f88041f0becc67a3ceac4fb1",
            "824d8eedf9fb41c9ae95b2c4d58685e4",
            "658fe3c22f044d9a8c46a46d410bac66",
            "ccad5071834640fb93efd4f0ef588ef5",
            "90aa4878cd3c42efad81cf2ce4c22dbf",
            "a55541ac5cc34f649b403afce097dc43",
            "6b92930599ad432d97c1dc3b3b6a6fe7",
            "7bffe1839d3d4f35839ea7b8a215eaea",
            "18e79a2153f84fc49968b41da0739984",
            "14fb80d9cc8e46049058df5de7c60afc",
            "72ef746e9aef4b1088ff585f4e4edee4",
            "62780c33a3094f518995b98610bc5b07",
            "4914769a78cb47c7ba239ff8e3b59d87",
            "0d8cea3727854229b20802e93e5750ef",
            "d67a697e90944554a307a7b0aeb63f00",
            "3edb54bc362c4985b12a3b679ea9eff8",
            "0b20baad42394a51ada13fd99a4f1c26",
            "ed65680bd3aa435985ee6cfdae2aa1dc",
            "974aae5e02194541951c3422190db8c3",
            "1e90809b17ca4e24ba948ac52fe1384b",
            "62df59650c454bd0bd253283b026e899",
            "3770b02040614db5803f1e81c8cdd434",
            "aa4db30245e443519afb66ae5abe813b",
            "bb75d1083cb84b1289a1d9edb3f39030",
            "c1bccad0c245493495dcd2f12c68049f",
            "2b75970d2c794a868da2448534647cdd",
            "8e213e8342184de68a5c048f9b26fded",
            "522799155f464469bc1b3565825a565a",
            "0027e00c277d44aa97a16c31c89c143f",
            "cb38aa2dc2594d2ba357a044a93524b7"
          ]
        }
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Training Progress:   0%|          | 0/20 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "93efb70d726a4d98b69a9fa610a23cf7"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Generating flow data:   0%|          | 0/49 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "18e79a2153f84fc49968b41da0739984"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Making gif:   0%|          | 0/50 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "1e90809b17ca4e24ba948ac52fe1384b"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "![4G](https://user-images.githubusercontent.com/15642823/266222225-c1021a63-53ed-4876-a9c2-2ae95d19bc93.gif)"
      ],
      "metadata": {
        "id": "uxaMg3uuTTF_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## 1 ring\n",
        "X_1 = np.random.multivariate_normal([0, 0], np.diag([5, 5]), 2000)\n",
        "X_1 = X_1[np.logical_and(np.sum(X_1 ** 2, axis=1) < 3.5 ** 2, np.sum(X_1 ** 2, axis=1) > 3 ** 2)]\n",
        "main(X_1, n_tvals=50, n_particles=10000, outdir=\"1ring\", epochs=100)\n"
      ],
      "metadata": {
        "id": "RIWkKz-FJ9W2",
        "outputId": "da0496a1-c939-4f33-bdc0-031a1a66587f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 568,
          "referenced_widgets": [
            "e3929859297f4b9eacf592b83f5d5629",
            "ee087bf7c04f468ca3611104d5aa09eb",
            "0775b2351474433c8c0002941c01e88d",
            "8b2f84b33a3840698986968056ce1a1c",
            "b2bd3c3b97b746088b2179226f70c28d",
            "2c479198437f4b238ad956a307721156",
            "e0f810c9da1f41a2a8716b99ddd74498",
            "3fae0ebb593e40248e2b71f3f24820df",
            "5a389525bea14c47bdb6aeff94a2a1fd",
            "f3fac88b259843e1bd79643f131ff8e0",
            "db76a2d3bb4a4f388dd3f0c9d5a50753",
            "13bc89f384034b5ba287789ef66d175a",
            "2046e86cd9c64c7682c80c727690a5cf",
            "08da24af969c4a13a563e3f8580c9949",
            "33d15071c4dd4ac2bfd84ab35e1a46ef",
            "6bb01c3cf44e4c06b00310a1a0d58fb3",
            "21eb55782ea74034a55a25dd71907d89",
            "0e14d80b399b468dad05e7bf5e767ca5",
            "85f93b563e834b489ce7ca4659392bdf",
            "2f16ee25e2bc4df188ff43d5c2e661c7",
            "4511c5daa97146a89920684044bbc0f3",
            "4d03794c43b34a1a86f07bbb4dbf3c35",
            "fae700d5981a46039ba8a01e4efde1ae",
            "30d81fdff4c14a8a84514ccf6577564a",
            "e5c7a8b39da3443d9c7f8f7828a5f03c",
            "7300215869b942c1a175286cb0ad3389",
            "3f79a861bd4a4066a94666c74ed78ac4",
            "930a54d5c32546c2893b7c9ae8faa06c",
            "1f7027915d8c4b6595fb3c7c9a4b7a74",
            "7e29719f63da418299da1b439318bc09",
            "cd5a2c1d3495451a8f9b5c72db3cb287",
            "a62cec9712fc4f0ba7805710a2e5a574",
            "c6781c68cf8f4342af80c1b57611d0c2"
          ]
        }
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Training Progress:   0%|          | 0/100 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "e3929859297f4b9eacf592b83f5d5629"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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