GitHub_collection_pykan/tutorials/Example/Example_13_phase_transition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5d904dee",
   "metadata": {},
   "source": [
    "# Example 13: Phase transition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6465ec94",
   "metadata": {},
   "source": [
    "In this example, we will use KAN to learn phase transitions in data. Phase transition is an important concept in science. We consider a toy example $f(x_1,x_2,x_3)$ is 1 if $g(x_1,x_2,x_3)>0$, and is 0 if $g(x_1,x_2,x_3)<0$. $g(x_1,x_2,x_3)={\\rm sin}(\\pi x_1)+{\\rm cos}(\\pi x_2)+{\\rm tan}(\\frac{\\pi}{2}x_3)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94056ef6",
   "metadata": {},
   "source": [
    "Intialize model and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0a59179d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cuda\n",
      "checkpoint directory created: ./model\n",
      "saving model version 0.0\n"
     ]
    }
   ],
   "source": [
    "from kan import KAN, create_dataset\n",
    "import torch\n",
    "\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
    "print(device)\n",
    "\n",
    "model = KAN(width=[3,1,1], grid=3, k=3, device=device)\n",
    "\n",
    "# create dataset\n",
    "f = lambda x: (torch.sin(torch.pi*x[:,[0]]) + torch.cos(torch.pi*x[:,[1]]) + torch.tan(torch.pi/2*x[:,[2]]) > 0).float()\n",
    "dataset = create_dataset(f, n_var=3, device=device)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3837440b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.5060, device='cuda:0')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.mean(dataset['train_label'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fe38f7c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 500x400 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model(dataset['train_input'])\n",
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8627b850",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.1\n"
     ]
    }
   ],
   "source": [
    "# set the last activation to be tanh\n",
    "model.fix_symbolic(1,0,0,'tanh',fit_params_bool=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3957140b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 500x400 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model(dataset['train_input'])\n",
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "be0b0daf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "| train_loss: 7.71e-02 | test_loss: 1.17e-01 | reg: 2.43e+02 | : 100%|█| 50/50 [00:09<00:00,  5.32it\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "saving model version 0.2\n"
     ]
    }
   ],
   "source": [
    "model.fit(dataset, opt=\"LBFGS\", steps=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2f9b37a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 500x400 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6d85bda",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}