{ "cells": [ { "cell_type": "markdown", "id": "fc571f68-3a5b-49d6-88d6-66ef6c2dab97", "metadata": {}, "source": [ "# Example: 1D Oscillator - Part 3/5\n", "\n", "- Author: Dr. Daning Huang\n", "- Date: 07/14/2025\n", "- Updated: 05/07/2026" ] }, { "cell_type": "markdown", "id": "7ac8fbcf-4201-4519-a33f-3ccd1b9bafc3", "metadata": {}, "source": [ "In this part of the example, we show the setup for data transformations on the input and observation data.\n", "\n", "Since Part 2 shows that KBF + weak form is a computationally economic choice, we will stick with this combination in this part." ] }, { "cell_type": "markdown", "id": "1d83f2b2-2290-47ae-ad7d-01fcf95965bd", "metadata": {}, "source": [ "## Preparation\n", "\n", "Same drill like in Part 2." ] }, { "cell_type": "code", "execution_count": 1, "id": "6e8f3d73-f86b-4ff3-ac79-17f695bd089e", "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings('ignore')\n", "import numpy as np\n", "import torch\n", "\n", "from dymad.io import load_model\n", "from dymad.models import KBF\n", "from dymad.training import WeakFormTrainer\n", "from dymad.utils import plot_trajectory, TrajectorySampler" ] }, { "cell_type": "code", "execution_count": 2, "id": "abd1ab44-5503-4bc2-9b0c-47701cfa6860", "metadata": {}, "outputs": [], "source": [ "B = 128 # Number of trajectories\n", "N = 501 # Number of steps\n", "t_grid = np.linspace(0, 5, N)\n", "\n", "A = np.array([\n", " [0., 1.],\n", " [-1., -0.1]])\n", "def f(t, z, u): # Define the dynamics\n", " return (z @ A.T) + u\n", "g = lambda t, z, u: z # Define the observation\n", "\n", "# Chirp input for training\n", "config_chr = {\n", " \"control\" : {\n", " \"kind\": \"chirp\",\n", " \"params\": {\n", " \"t1\": 4.0,\n", " \"freq_range\": (0.5, 2.0),\n", " \"amp_range\": (0.5, 1.0),\n", " \"phase_range\": (0.0, 360.0)}}}\n", "\n", "# Random Gaussian input for testing/generalization\n", "config_gau = {\n", " \"control\" : {\n", " \"kind\": \"gaussian\",\n", " \"params\": {\n", " \"mean\": 0.5,\n", " \"std\": 1.0,\n", " \"t1\": 4.0,\n", " \"dt\": 0.2,\n", " \"mode\": \"zoh\"}}}\n", "\n", "# Generate data\n", "sampler_chr = TrajectorySampler(f, g, config='lti_data.yaml', config_mod=config_chr)\n", "ts, zs, us, xs = sampler_chr.sample(t_grid, batch=B, save='./data/lti.npz')\n", "\n", "sampler_gau = TrajectorySampler(f, g, config='lti_data.yaml', config_mod=config_gau)" ] }, { "cell_type": "markdown", "id": "fb53352a-86df-4df9-aa6e-e14690854059", "metadata": {}, "source": [ "Set up the options for weak form." ] }, { "cell_type": "code", "execution_count": 3, "id": "65612056-38a2-453f-9065-1d117e42f69e", "metadata": {}, "outputs": [], "source": [ "opt_wf = {\n", " \"model\": {\n", " \"name\" : 'lti_kbf_wf',\n", " \"encoder_layers\" : 1,\n", " \"decoder_layers\" : 1,\n", " \"hidden_dimension\" : 32,\n", " \"koopman_dimension\" : 4,\n", " \"const_term\" : True,\n", " \"activation\" : \"none\",\n", " \"weight_init\" : \"xavier_uniform\",\n", " \"input_order\" : \"cubic\"\n", " },\n", " \"criterion\": {\n", " \"dynamics\" : {\"weight\" : 1.0},\n", " \"recon\" : {\"weight\" : 1.0}\n", " },\n", " \"phases\" : [{\n", " \"type\": \"optimizer\",\n", " \"name\": \"WeakForm\",\n", " \"trainer\": \"Weak\",\n", " \"n_epochs\": 500,\n", " \"save_interval\": 10,\n", " \"load_checkpoint\": False,\n", " \"learning_rate\": 5e-3,\n", " \"decay_rate\": 0.999,\n", " \"weak_form_params\": {\n", " \"N\": 13,\n", " \"dN\": 2,\n", " \"ordpol\": 2,\n", " \"ordint\": 2}\n", " }]\n", "}" ] }, { "cell_type": "markdown", "id": "1b414672-40c9-4c4a-ac1c-8d1ade19c0d4", "metadata": {}, "source": [ "## Data Transformation\n", "\n", "We will run 3 cases, with transformations specified below:\n", "\n", "- No transformation, as in the current `lti_model.yaml`\n", "- `x` transforms by standard deviation, `u` transforms to [0, 1]\n", "- `x` transforms by standard deviation **plus** a time delay of 1, `u` transforms by a time delay of 1\n", "\n", "In the last case, a list is used for `x` to indicate the sequence of transform." ] }, { "cell_type": "code", "execution_count": 4, "id": "5e48538c-7524-44fb-9caa-a79dc9b222de", "metadata": {}, "outputs": [], "source": [ "trans1 = {\n", " \"transform_x\": {\"type\": \"identity\"},\n", " \"transform_u\": {\"type\": \"identity\"}}\n", "\n", "trans2 = {\n", " \"transform_x\": {\"type\": \"scaler\", \"mode\": \"std\"},\n", " \"transform_u\": {\"type\": \"scaler\", \"mode\": \"01\"}}\n", "\n", "trans3 = {\n", " \"transform_x\": [\n", " {\"type\": \"scaler\", \"mode\": \"std\"},\n", " {\"type\": \"delay\", \"delay\": 1}],\n", " \"transform_u\": {\"type\": \"delay\", \"delay\": 1}}" ] }, { "cell_type": "markdown", "id": "41b006f0-1fa8-4008-b9d7-b71d29c15285", "metadata": {}, "source": [ "Now Case 1 as a baseline.\n", "\n", "The effect of data transformation can be seen in the figure generated on the fly, `lti_kbf_wf_prediction.png`. Note the range of `x` and `u`." ] }, { "cell_type": "code", "execution_count": 5, "id": "1af6b3e0-d8b3-4fc4-ac67-52379ef42777", "metadata": {}, "outputs": [], "source": [ "config_path = 'lti_model.yaml'\n", "opt_wf.update(**trans1)\n", "trainer = WeakFormTrainer(config_path, KBF, config_mod=opt_wf)\n", "trainer.train();" ] }, { "cell_type": "markdown", "id": "b2879ea0-47e4-48ba-a843-1146e5f863a5", "metadata": {}, "source": [ "Then Case 2. Clearly the ranges of `x` and `u` are different." ] }, { "cell_type": "code", "execution_count": 6, "id": "59804fbf-37b5-4302-876d-cfd45ea4d1c9", "metadata": {}, "outputs": [], "source": [ "opt_wf.update(**trans2)\n", "trainer = WeakFormTrainer(config_path, KBF, config_mod=opt_wf)\n", "trainer.train();" ] }, { "cell_type": "markdown", "id": "a10c2bfb-fab6-4318-ad6a-c69fd14975b2", "metadata": {}, "source": [ "Lastly, Case 3. In this case, there are more \"states\" and \"inputs\" perceived by the model, due to the time delay.\n", "\n", "> With time delay, we can also use SDM (Sequential Dynamics Models), that leverage recurrent NN's. This will be explored in the later part of this example." ] }, { "cell_type": "code", "execution_count": 7, "id": "d2f7c8c3-1f92-4aec-ae08-f5243bba265b", "metadata": {}, "outputs": [], "source": [ "opt_wf.update(**trans3)\n", "trainer = WeakFormTrainer(config_path, KBF, config_mod=opt_wf)\n", "trainer.train();" ] }, { "cell_type": "markdown", "id": "8b7ba2b8-1948-4cdc-a991-508258c6519e", "metadata": {}, "source": [ "We also show the model prediction for Case 3. The tiny change here is in `prd_wf`, where `t_data` is reduced by 1 step, due to the time delay.\n", "\n", "The prediction function generated by `load_model` actually performs a transform and inverse transform on the given `x` and `u`, so that one does not need to manually perform the transformation for every new prediction." ] }, { "cell_type": "code", "execution_count": 8, "id": "cd1884ea-fc04-4d9f-9ded-1b660da7edec", "metadata": {}, "outputs": [], "source": [ "ts, xs, us, ys = sampler_gau.sample(t_grid, batch=1, save=None)\n", "x_data = xs[0]\n", "t_data = ts[0]\n", "u_data = us[0]" ] }, { "cell_type": "code", "execution_count": 10, "id": "cff2d74a-2f31-451f-92a5-f6534c90fc8f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mdl_wf, prd_wf = load_model(KBF, 'lti_kbf_wf.pt')\n", "\n", "with torch.no_grad():\n", " weak_pred = prd_wf(x_data[:2], t_data[:-1], u=u_data)\n", "\n", "plot_trajectory(\n", " np.array([x_data, weak_pred]), t_data, \"LTI\",\n", " us=u_data, labels=['Truth', 'WF'], ifclose=False);" ] } ], "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 }