{ "cells": [ { "cell_type": "markdown", "id": "cfd277cb-8781-446e-9c1d-82ea235079d5", "metadata": {}, "source": [ "# Example: Cylinder Flow - Part 1/3\n", "\n", "- Author: Dr. Daning Huang\n", "- Date: 10/11/2025\n", "- Updated: 05/07/2026" ] }, { "cell_type": "markdown", "id": "fc158844-a2f3-4905-b07b-dad6d1b99f22", "metadata": {}, "source": [ "## Introduction\n", "\n", "In this example we will look at the cylinder flow problem, which has been a classical benchmark case for many dynamics learning algorithms.\n", "\n", "- We will start with the functionalities in `DyMAD` that help exploring the data properties.\n", "- Then we will use several model architectures to learn the dynamics, and visualize the results.\n", "- Lastly we will manipulate the learned model to extract some dynamics-related information, and visualize the results." ] }, { "cell_type": "markdown", "id": "174929bf-c31f-4c73-b93e-47bbba4cb540", "metadata": {}, "source": [ "## Setup\n", "\n", "Some imports, and the split of dataset. If you only have the original `CYLINDER_ALL.mat` file, place it under `examples/vortex/data/`, then run `cd examples/vortex/data && python ../../../scripts/vortex/data/data_extract.py` so this notebook can load `./data/raw.npz`. The train/test split will be used in later parts, so we reload the processed datasets in the end." ] }, { "cell_type": "code", "execution_count": 1, "id": "33a065c1-99f8-4b73-b808-2ffdfb137238", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import numpy as np\n", "\n", "from dymad.io import DataInterface\n", "from dymad.numerics import DimensionEstimator\n", "from dymad.utils import compare_contour, plot_contour" ] }, { "cell_type": "code", "execution_count": null, "id": "d17980ca-fbe3-4ea0-b1cb-2379c0266895", "metadata": {}, "outputs": [], "source": [ "raw = np.load('./data/raw.npz')['vor']\n", "Nt, Nx, Ny = raw.shape\n", "ts = np.arange(Nt)\n", "dt = 1.\n", "X = raw.reshape(Nt, -1)\n", "\n", "Nspl = 140\n", "np.savez_compressed('data/cylinder.npz', x=X[:Nspl], t=ts[:Nspl])\n", "np.savez_compressed('data/test.npz', x=X[Nspl:], t=ts[Nspl:])" ] }, { "cell_type": "code", "execution_count": 3, "id": "e1430e3a-c658-4b74-8af4-0ad26ec37e3b", "metadata": {}, "outputs": [], "source": [ "config_path = 'vor_model.yaml'\n", "Nx, Ny = 199, 449\n", "\n", "dat = np.load('data/cylinder.npz')\n", "ttrn, Xtrn = dat['t'], dat['x']\n", "dt = ttrn[1] - ttrn[0]\n", "\n", "dat = np.load('data/test.npz')\n", "ttst, Xtst = dat['t'], dat['x']" ] }, { "cell_type": "code", "execution_count": null, "id": "c9e7adf9-e890-41d4-aac1-8f2e2979dc00", "metadata": {}, "outputs": [], "source": [ "\"\"\"vor_model.yaml\n", "data:\n", " path: './data/cylinder.npz'\n", " n_samples: 1\n", " n_steps: 140\n", " double_precision: true\n", "\n", "transform_x:\n", " - type: \"svd\"\n", " ifcen: true\n", " order: 12\n", " - type: \"scaler\"\n", " mode: \"std\"\n", "\n", "split:\n", " train_frac: 1\n", "\n", "dataloader:\n", " batch_size: 1\n", "\n", "plotting:\n", " xidx: [0, 1, 2, 3]\n", "\"\"\"" ] }, { "cell_type": "markdown", "id": "39ab24dd-9b95-4521-ab79-bc3fad3debdd", "metadata": {}, "source": [ "## Data Transformations\n", "\n", "### The DataInterface class\n", "\n", "Recall in model YAML files, the `transform_x` entry defines a series of transforms to pre-process the data before training, and transform the model prediction back to the original data space. This functionality is available in a standalone mode via the `DataInterface` class, so that the user can explore the structure of the data to inform the choice of model architecture.\n", "\n", "Below, as an example to showcase the methods in `DataInterface`, we consider a two-step transformation: first by SVD, then by Diffusion Map (DM). The DM is a nonlinear dimension reduction algorithm, whose inverse is highly nonlinear; here the Generalized Moving Least Squares (GMLS) method is used as the inverse. See `dymad/transform/ndr.py::TransformKernel` for the meanings of the parameters." ] }, { "cell_type": "code", "execution_count": 5, "id": "766867fe-3377-4ea6-8dea-f7589c3336f4", "metadata": {}, "outputs": [], "source": [ "trn_svd = {\n", " \"type\" : \"svd\",\n", " \"ifcen\": True, # Center the data, i.e., remove the mean\n", " \"order\": 0.9999 # Retain 99.99% energy\n", "}\n", "trn_dmf = {\n", " \"type\" : \"dm\",\n", " \"edim\": 3, # Embedding dimension of 3\n", " \"Knn\" : 15,\n", " \"Kphi\": 3,\n", " \"inverse\": \"gmls\",\n", " \"order\": 1,\n", " \"mode\": \"full\"\n", "}" ] }, { "cell_type": "markdown", "id": "6d753c8c-c63a-4d4c-a3d7-4aaf61d2dc48", "metadata": {}, "source": [ "First instantiate a `DataInterface` object, whose syntax is close to `Trainer` classes; upon instantiation it will fit the `Transform` objects given the data in `config` (the training data in our case). Then apply the transform to the training and test data." ] }, { "cell_type": "code", "execution_count": 6, "id": "415a9feb-a2ef-4289-b321-0aa703aa46a5", "metadata": {}, "outputs": [], "source": [ "di = DataInterface(config_path=config_path, config_mod={\"transform_x\" : [trn_svd, trn_dmf]})\n", "Ztrn = di.encode(Xtrn)\n", "Ztst = di.encode(Xtst)\n", "Xrec = di.decode(Ztst) # Transform back" ] }, { "cell_type": "markdown", "id": "32cf6498-4ea8-466a-b7d0-2075e6bc9425", "metadata": {}, "source": [ "Now the data is encoded in a 3D latent space, and the latent coordinates are plotted against time as below. The test data follows the trend of training data well, indicating the chosen transformations are reasonable. Furthermore, the first coordinate is flat, and the rest seem to follow a harmonic trend - this indicates that the data live on a simple circle-like manifold, which is visually verified in the 3D plot below." ] }, { "cell_type": "code", "execution_count": 7, "id": "4d5d809f-f881-4488-8b46-ab06c923f0f1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stys = ['b-', 'r-', 'k-']\n", "f = plt.figure()\n", "for _i in range(3):\n", " plt.plot(ttrn, Ztrn[:,_i], stys[_i], label=f'DM coord {_i+1}')\n", " plt.plot(ttst, Ztst[:,_i], stys[_i]+'-')\n", "plt.xlabel('t'); plt.ylabel('z'); plt.legend();" ] }, { "cell_type": "code", "execution_count": 8, "id": "e148cadd-fb08-40d7-99a7-f7eb84d3db09", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = plt.figure()\n", "ax = f.add_subplot(111, projection='3d')\n", "ax.plot(*Ztrn.T, 'b.');" ] }, { "cell_type": "markdown", "id": "1839b992-e42d-4b5d-9211-4ae53c651408", "metadata": {}, "source": [ "As a sanity check, we compare the truth and the reconstructed data at a certain time. Clearly the error is nearly zero." ] }, { "cell_type": "code", "execution_count": 9, "id": "1e850bda-4252-4110-a89f-b2730edfa1c2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "idx = 5\n", "x_tru = Xtst[idx].reshape(Nx, Ny)\n", "x_rec = Xrec[idx].reshape(Nx, Ny)\n", "f, ax = compare_contour(x_tru, x_rec, vmin=-4, vmax=4, figsize=(12, 2))\n", "for _a in ax:\n", " _a.set_axis_off()" ] }, { "cell_type": "markdown", "id": "47966de1-c7ea-49c0-97f3-ca5209e2c71c", "metadata": {}, "source": [ "### Intrinsic dimension estimation\n", "\n", "To quantitatively determine the intrinsic dimension of the data, `DyMAD` also has a `DimensionEstimator` class, that uses a kernel-based algorithm. Once we round up the estimation, it is 1D.\n", "\n", "> Note that \"intrinsic\" dimension is the dimension of a \"local patch\" of data, and is often smaller than the latent dimension. For example, in a circular data, the latent dimension is 2 (or higher), but its local patch is just an arc, that is 1D; hence the circular structure is intrinsically 1D." ] }, { "cell_type": "code", "execution_count": 10, "id": "a8f44ab2-f187-43b6-985f-ab794f8e327c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated intrinsic dimension: 1\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "e1 = DimensionEstimator(data=Xtrn, Knn=10, bracket=[-20, 5], tol=0.2)\n", "dim = e1()\n", "print(f\"Estimated intrinsic dimension: {dim}\")\n", "e1.plot(N=50);" ] }, { "cell_type": "markdown", "id": "d59fc266-a56d-4f8c-b152-19c1fcbad3ce", "metadata": {}, "source": [ "Here is also a sanity check by the local PCA method. For each data point, the method takes the neighboring points, computes the difference, and performs SVD; the distributions of singular values are overlayed in blue (solid line as average and shade as +/- 1 std). The first singular value dominates the distribution, indicating one dominant dimension.\n", "\n", "As a reference, the red dashed line is the singular values obtained from the full dataset, which has a much longer tail than the local one." ] }, { "cell_type": "code", "execution_count": 11, "id": "2d265a10-eb8e-439c-ab06-76922808d79a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "e1.sanity_check()\n", "plt.xlim([0, 20]);" ] }, { "cell_type": "markdown", "id": "fbcc83ae-9e45-431d-add1-f4be5b01bde4", "metadata": {}, "source": [ "## Further Data Manipulations\n", "\n", "### Step-by-step transforms\n", "\n", "The data transformations can be done step by step, to probe the intermediate results.\n", "\n", "This is done by specifying a `rng` argument. Think it as `range(*rng)`, so `rng=[0,1]` uses `range(0,1)=[0]` - the first transform (from data to SVD in our case); similarly `[1,2]` uses the second transform (from SVD to DM)." ] }, { "cell_type": "code", "execution_count": 12, "id": "8c149053-89db-4697-a5fe-89e783b92d69", "metadata": {}, "outputs": [], "source": [ "Zsvd = di.encode(Xtst, rng=[0,1]) # Data -> SVD\n", "Zdmf = di.encode(Zsvd, rng=[1,2]) # SVD -> DM\n", "Xsvd = di.decode(Zdmf, rng=[1,2]) # DM -> SVD" ] }, { "cell_type": "markdown", "id": "073f1281-d130-4149-b85c-05721ec7a421", "metadata": {}, "source": [ "At the SVD step, we can extract out and plot the modes, which is done by `get_backward_modes`. Below the first 5 modes are shown. The higher order modes correspond to the long tail in global singular values shown earlier. The modes are scaled for better visualization." ] }, { "cell_type": "code", "execution_count": 13, "id": "ae057a84-3b83-42f8-afb9-1f58bb8040de", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "modes_s = di.get_backward_modes(ref=Xsvd[idx], rng=[0,1]).reshape(-1, Nx, Ny)\n", "ref = Xtst[idx].reshape(1, Nx, Ny)\n", "arrays = np.concatenate([ref, 200*modes_s[:5]], axis=0)\n", "labels = [f'step {idx}'] + [f'mode {_i+1}' for _i in range(5)]\n", "f, ax = plot_contour(arrays,\n", " figsize=(12, 4), vmin=-4, vmax=4, colorbar=True, label=labels, grid=(2, 3), mode='contourf')\n", "for _a in ax.flatten():\n", " _a.set_axis_off()" ] }, { "cell_type": "markdown", "id": "bcea5d0d-52b7-450b-a130-6c6b78fc4249", "metadata": {}, "source": [ "### Forward and backward modes\n", "\n", "In the previous discussion, we used `get_backward_modes`. As one might guess, there is also `get_forward_modes`. Their precise definitions are the following:\n", "\n", "- In the forward transform, i.e., encoding, say $z=f(x)$, the forward modes are defined as $dz/dx$, which describes how sensitive is $z$ to each entry in $x$.\n", " + Use SVD as example: $z=f(x)=U^\\top (x-x_0)$, so the forward modes are $U^\\top$.\n", "- In the backward transform, i.e., decoding, say $x=g(z)$, the backward modes are defined as $dx/dz$, which describes how sensitive is $x$ to each entry in $z$.\n", " + SVD example again: $x=g(z)=Uz+x_0$, so the backward modes are $U$.\n", " + Note that in `DyMAD` the transpose of backward modes are returned." ] }, { "cell_type": "markdown", "id": "6cf10a0a-2aa7-4bb8-87c5-5bd6729e44c9", "metadata": {}, "source": [ "Below let's first look at the backward modes of the combined SVD-DM transform. Note that for nonlinear transforms, the derivatives are dependent on the data sample.\n", "\n", "There are three latent variables, so there are 3 modes. Mode 1 appears all 0, because $z_1$ is flat and insensitive to any change in $x$. Modes 2 and 3 are somewhat similar, and only differ in magnitude. This is due to our implementation, that accounts for the manifold constraint that the data intrinsic dimension is 1; this actually results in collinearity of modes 2 and 3.\n", "\n", "> One can change the manifold constraint by setting `order` to 2 or 3 in `trn_dmf`." ] }, { "cell_type": "code", "execution_count": 14, "id": "12190fcb-705b-4c17-b396-c286998a957d", "metadata": {}, "outputs": [], "source": [ "modes_b = di.get_backward_modes(ref=Zdmf[idx]).reshape(-1, Nx, Ny)" ] }, { "cell_type": "code", "execution_count": 15, "id": "669de057-7ddf-4fd7-89ae-fb1324c02613", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "arrays = np.concatenate([ref, modes_b], axis=0)\n", "labels = [f'step {idx}'] + [f'mode {_i+1}' for _i in range(3)]\n", "f, ax = plot_contour(arrays, vmin=-4, vmax=4,\n", " figsize=(8, 4), colorbar=True, label=labels, grid=(2, 2), mode='contourf')\n", "for _a in ax.flatten():\n", " _a.set_axis_off()" ] }, { "cell_type": "markdown", "id": "d07454d6-241e-4532-abb7-4ae45fd64fac", "metadata": {}, "source": [ "To understand the backward modes more, note that $\\dot{x} = (dx/dz) \\dot{z}$. So the modes relate the rate of change in $z$ to that in $x$. We can numerically verify this as below - fairly close, up to some inevitable numerical errors." ] }, { "cell_type": "code", "execution_count": 16, "id": "eafd1ee8-5e26-41cc-9700-e21c45ad8068", "metadata": {}, "outputs": [], "source": [ "dXrf = (Xtst[idx+1] - Xtst[idx-1]) / (2*dt) # Estimate \\dot{x} by central difference\n", "dXrf = dXrf.reshape(1, Nx, Ny)\n", "dZrf = (Zdmf[idx+1] - Zdmf[idx-1]) / (2*dt) # Estimate \\dot{z} by central difference\n", "dXdt = np.sum(dZrf[:,None,None] * modes_b, axis=0, keepdims=True) # Compute \\dot{x} by backward modes" ] }, { "cell_type": "code", "execution_count": 17, "id": "1e740889-34bf-49e4-a97d-3109a0db6713", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = compare_contour(dXrf[0], dXdt[0], figsize=(12, 2))\n", "for _a in ax:\n", " _a.set_axis_off()" ] }, { "cell_type": "markdown", "id": "41d54248-ec43-4c60-bd9a-d92db289787e", "metadata": {}, "source": [ "With the understanding in backward mode, the forward mode should be relatively straightforward. In the contours below, again mode 1 is nearly zero, and modes 2 and 3 appear collinear. Note the modes are scaled for better visualization." ] }, { "cell_type": "code", "execution_count": 18, "id": "ee986fd8-1187-40c7-8590-6dfd6f975ca1", "metadata": {}, "outputs": [], "source": [ "modes_f = di.get_forward_modes(ref=Xtst[idx]).reshape(-1, Nx, Ny)" ] }, { "cell_type": "code", "execution_count": 19, "id": "527590cf-ab0d-42fc-a8f1-772e74e36dcc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "arrays = np.concatenate([ref, 40000*modes_f], axis=0)\n", "labels = [f'step {idx}'] + [f'mode {_i+1}' for _i in range(3)]\n", "f, ax = plot_contour(arrays, vmin=-4, vmax=4,\n", " figsize=(8, 4), colorbar=True, label=labels, grid=(2, 2), mode='contourf')\n", "for _a in ax.flatten():\n", " _a.set_axis_off()" ] }, { "cell_type": "markdown", "id": "378af660-f9e8-487a-bf20-c3d3b38ed862", "metadata": {}, "source": [ "Similarly we verify the relation $\\dot{z} = (dz/dx) \\dot{x}$. It is only three components, so we show in barplots. The first entry is zero, so no bar is show. The rest components are again fairly close." ] }, { "cell_type": "code", "execution_count": 20, "id": "3f2219a9-05ef-45fc-b408-ea60dad8ad21", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dZdt = np.sum(dXrf * modes_f, axis=(1,2))\n", "\n", "f = plt.figure(figsize=(4,3))\n", "labels = ['1', '2', '3']\n", "values = np.stack([dZdt, dZrf], axis=1) # shape (3,2)\n", "x = np.arange(len(labels))\n", "width = 0.35\n", "plt.bar(x - width/2, values[:,0], width, label='Estimate', color='blue')\n", "plt.bar(x + width/2, values[:,1], width, label='Finite Diff.', color='orange')\n", "plt.xticks(x, labels)\n", "plt.legend()\n", "plt.ylabel('Rate');" ] }, { "cell_type": "markdown", "id": "d685b7e3-9885-4b7a-969f-75446cdb81b1", "metadata": {}, "source": [ "One thing that one may have noted is the difference in the magnitudes in the modes. The forward modes are *tiny*.\n", "\n", "One way to think about this is the following: All entries of $x$ and $z$ are $O(1)$, but $dim(x)$ is $O(10^4)$; if $z=Ax$ then we must have entries of $A$ as $O(10^{-4})$ to maintain the correct order of magnitude.\n", "\n", "Also, one may verify that the tiny forward modes are \"compatible\" with backward modes, by noting that $(dz/dx)(dx/dz)=I$ if both terms are full rank. This product is in the first plot below. In our case the modes are rank-1, so we end up with one dominant entry.\n", "\n", "Furthermore, one can also explore the forward and backward modes themselves. For example, in forward, note the identity\n", "$$\n", "\\|\\dot{x}\\|^2 = \\left\\|\\frac{dx}{dz}\\dot{z}\\right\\|^2 = \\dot{z}^\\top\\left(\\frac{dx}{dz}\\right)^\\top\\frac{dx}{dz}\\dot{z} \\equiv \\dot{z}^\\top M \\dot{z}\n", "$$\n", "So the product $M$ is a \"metric\" that converts the size of $\\dot{z}$ to that of $\\dot{x}$. From the plot below, we can also see it is mainly $z_2$ that is contributing to the change in $x$ at the given time." ] }, { "cell_type": "code", "execution_count": null, "id": "c3ce0331-8a18-4998-b6c8-a15376c291b1", "metadata": {}, "outputs": [], "source": [ "_f = modes_f.reshape(3, -1)\n", "_b = modes_b.reshape(3, -1)\n", "fb = _f @ _b.T\n", "ff = _f @ _f.T\n", "bb = _b @ _b.T" ] }, { "cell_type": "code", "execution_count": 22, "id": "36b06afc-35ac-4eda-b527-09a01fde5ef6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, ax = plt.subplots(1, 3, figsize=(9, 3))\n", "im0 = ax[0].imshow(fb, vmin=-1, vmax=1, cmap='bwr')\n", "ax[0].set_title('dz/dx * dx/dz')\n", "plt.colorbar(im0, ax=ax[0])\n", "\n", "im1 = ax[1].imshow(ff, cmap='bwr')\n", "ax[1].set_title('dz/dx * (dz/dx)^T')\n", "plt.colorbar(im1, ax=ax[1])\n", "\n", "im2 = ax[2].imshow(bb, cmap='bwr')\n", "ax[2].set_title('(dx/dz)^T * dx/dz')\n", "plt.colorbar(im2, ax=ax[2]);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 5 }