167 lines
13 KiB
Plaintext
167 lines
13 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "134e7f9d",
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"metadata": {},
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"source": [
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"# Physics 2A: Conservation Laws"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "fd0d2987",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"checkpoint directory created: ./model\n",
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"saving model version 0.0\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"| train_loss: 1.07e-04 | test_loss: 1.17e-04 | reg: 4.12e+00 | : 100%|█| 20/20 [00:01<00:00, 16.52it"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"saving model version 0.1\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\n"
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]
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}
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],
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"source": [
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"from kan import *\n",
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"from kan.utils import batch_jacobian, create_dataset_from_data\n",
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"import numpy as np\n",
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"\n",
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"model = KAN(width=[2,1], seed=42)\n",
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"\n",
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"# the model learns the Hamiltonian H = 1/2 * (x**2 + p**2)\n",
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"x = torch.rand(1000,2) * 2 - 1\n",
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"flow = torch.cat([x[:,[1]], -x[:,[0]]], dim=1)\n",
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"\n",
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"def pred_fn(model, x):\n",
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" grad = batch_jacobian(model, x, create_graph=True)\n",
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" grad_normalized = grad/torch.linalg.norm(grad, dim=1, keepdim=True)\n",
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" return grad_normalized\n",
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"\n",
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"loss_fn = lambda grad_normalized, flow: torch.mean(torch.sum(flow * grad_normalized, dim=1)**2)\n",
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"\n",
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"\n",
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"dataset = create_dataset_from_data(x, flow)\n",
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"model.fit(dataset, steps=20, pred_fn=pred_fn, loss_fn=loss_fn);"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "60c88d7f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 500x200 with 4 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"model.plot()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "e8cb9a2f",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"fixing (0,0,0) with x^2, r2=1.0000003576278687, c=2\n",
|
|
"fixing (0,1,0) with x^2, r2=1.0000004768371582, c=2\n",
|
|
"saving model version 0.2\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"model.auto_symbolic()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "1b143bf8",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle - 1.191 x_{1}^{2} - 1.191 x_{2}^{2} + 2.329$"
|
|
],
|
|
"text/plain": [
|
|
"-1.191*x_1**2 - 1.191*x_2**2 + 2.329"
|
|
]
|
|
},
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"from kan.utils import ex_round\n",
|
|
"ex_round(model.symbolic_formula()[0][0], 3)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "782f818f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
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