ODENet.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e747be42",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as npr\n",
    "import jax.numpy as jnp\n",
    "from jax import jit, grad\n",
    "from jax import vmap\n",
    "from scipy.optimize import curve_fit\n",
    "from jax.experimental.ode import odeint\n",
    "from jax.scipy.optimize import minimize\n",
    "from scipy.optimize import minimize as _minimize_\n",
    "from scipy.integrate import odeint as _odeint_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59a9dd97",
   "metadata": {},
   "source": [
    "# Toy Example\n",
    "\n",
    "From http://implicit-layers-tutorial.org/neural_odes/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a1f565e",
   "metadata": {},
   "source": [
    "### Toy dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "41ecf4b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 432,
       "width": 578
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Toy 1D dataset.\n",
    "x = jnp.reshape(jnp.linspace(-2.0, 2.0, 10), (10, 1))\n",
    "y = x**3 + 0.1 * x\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86b172b8",
   "metadata": {},
   "source": [
    "### MLP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "72ea393a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mlp(params, x):\n",
    "    # A multi-layer perceptron, i.e. a fully-connected neural network.\n",
    "    for w, b in params:\n",
    "        y = jnp.dot(x, w) + b  # Linear transform\n",
    "        x = jnp.tanh(y)        # Nonlinearity\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "74568f16",
   "metadata": {},
   "outputs": [],
   "source": [
    "param_scale = 1.0\n",
    "\n",
    "def init_random_params(scale, layer_sizes, rng=npr.RandomState(0)):\n",
    "    return [\n",
    "        (scale * rng.randn(m, n), scale * rng.randn(n))\n",
    "        for m, n, in zip(layer_sizes[:-1], layer_sizes[1:])\n",
    "    ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a482e180",
   "metadata": {},
   "source": [
    "### ResNet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "41181a7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def resnet(params, x, depth):\n",
    "    for i in range(depth):\n",
    "        y = mlp(params, x) + x\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ee570bc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "resnet_depth = 3\n",
    "def resnet_loss(params, x, y):\n",
    "    yhat = resnet(params, x, resnet_depth)\n",
    "    return jnp.mean((yhat - y)**2)\n",
    "\n",
    "def init_random_params(scale, layer_sizes, rng=npr.RandomState(0)):\n",
    "    return [(scale * rng.randn(m, n), scale * rng.randn(n))\n",
    "          for m, n, in zip(layer_sizes[:-1], layer_sizes[1:])]\n",
    "\n",
    "# A simple gradient-descent optimizer.\n",
    "@jit\n",
    "def resnet_update(params, x, y):\n",
    "    grads = grad(resnet_loss)(params, x, y)\n",
    "    return [\n",
    "        (w - η * dw, b - η * db)\n",
    "        for (w, b), (dw, db) in zip(params, grads)\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8b3154d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hyperparameters.\n",
    "layer_sizes = [1, 20, 1]\n",
    "η = 0.01\n",
    "train_iters = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5562c7a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize and train.\n",
    "resnet_params = init_random_params(param_scale, layer_sizes)\n",
    "for i in range(train_iters):\n",
    "    resnet_params = resnet_update(resnet_params, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50c2bdfe",
   "metadata": {},
   "source": [
    "### ODENet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "eac4d8c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_dynamics(y, t, params):\n",
    "    y_and_t = jnp.hstack([y, jnp.array(t)])\n",
    "    return mlp(params, y_and_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2e26d583",
   "metadata": {},
   "outputs": [],
   "source": [
    "def odenet(params, y0, t=jnp.array([0.0, 1.0])):\n",
    "    _, y1 = odeint(nn_dynamics, y0, t, params)\n",
    "    return y1\n",
    "\n",
    "odenet = vmap(odenet, in_axes=(None, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2a966226",
   "metadata": {},
   "outputs": [],
   "source": [
    "def odenet_loss(params, x, y):\n",
    "    yhat = odenet(params, x)\n",
    "    return jnp.mean((yhat - y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7862e649",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit\n",
    "def odenet_update(params, x, y):\n",
    "    grads = grad(odenet_loss)(params, x, y)\n",
    "    return [\n",
    "        (w - η * dw, b - η * db)\n",
    "        for (w, b), (dw, db) in zip(params, grads)\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "63c24874",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We need to change the input dimension to 2, to allow time-dependent dynamics.\n",
    "odenet_layer_sizes = [2, 20, 1]\n",
    "\n",
    "# Initialize \n",
    "odenet_params = init_random_params(param_scale, odenet_layer_sizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "612f1b77",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "for i in range(train_iters):\n",
    "    odenet_params = odenet_update(odenet_params, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0e045a5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "for i in range(train_iters):\n",
    "    odenet_params = odenet_update(odenet_params, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54727f44",
   "metadata": {},
   "source": [
    "### Compare ResNet and ODENet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "174412b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "resent =  0.10412481 odenet =  0.0023549802\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 554,
       "width": 814
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\n",
    "    'resent = ', resnet_loss(resnet_params, x, y),\n",
    "    'odenet = ', odenet_loss(odenet_params, x, y)\n",
    ")\n",
    "\n",
    "# Plot resulting model.\n",
    "fig = plt.figure(figsize=(6, 4), dpi=150)\n",
    "ax = fig.gca()\n",
    "ax.scatter(x, y, lw=0.5, label='data')\n",
    "fine_x = jnp.reshape(jnp.linspace(-3.0, 3.0, 100), (100, 1))\n",
    "ax.plot(fine_x, resnet(resnet_params, fine_x, resnet_depth), lw=0.5, label='resent')\n",
    "ax.plot(fine_x, odenet(odenet_params, fine_x), lw=0.5, label='odenet')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46afbc14",
   "metadata": {},
   "source": [
    "# Logistic equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "38618bea",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic(t, y0, r, K):\n",
    "    return K / (1 - (1 - K/y0) * jnp.exp(-r * t))\n",
    "\n",
    "def logistic_loss(params, t, y):\n",
    "    yhat = logistic(t, *params)\n",
    "    return jnp.mean((yhat - y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "31dfbb2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 1.2\n",
    "r = 0.5\n",
    "y0 = 0.2\n",
    "reps = 5\n",
    "t = jnp.linspace(0, 24, 24*2)\n",
    "t = jnp.array([t]*reps).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4514f815",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = logistic(t, y0, r, K) + npr.normal(0, 0.02, size=t.shape)\n",
    "y = y.squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "96398c1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 432,
       "width": 567
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t.T, y.T, '-k', alpha=1/reps)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.xlim(0, 24);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9bc453a",
   "metadata": {},
   "source": [
    "### Curve fitting the equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a90fea92",
   "metadata": {},
   "outputs": [],
   "source": [
    "params_guess = jnp.array([y.min(), 1, y.max()])\n",
    "params, pcov = curve_fit(logistic, t.ravel(), y.ravel(), params_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fc2e1565",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2 0.5 1.2 | 0.00040311948\n",
      "0.20128386981070637 0.4991952381803526 1.2042213722496522 | 0.0003895881\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 552
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(y0, r, K, '|', logistic_loss((y0, r, K), t, y))\n",
    "print(*params, '|', logistic_loss(params, t, y))\n",
    "\n",
    "plt.plot(t, y, '.k')\n",
    "plt.plot(t.T, logistic(t, *params).T, '-r');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "438fbccb",
   "metadata": {},
   "source": [
    "### Curve fitting the logistic ODE - JAX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "56ee0f0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic_ode(y, t, r, K):\n",
    "    return r * y * (1 - y/K)\n",
    "\n",
    "def logistic_odeint(t, y0, r, K):\n",
    "    return odeint(logistic_ode, y0, t, r, K)\n",
    "\n",
    "# plt.plot(t[0], logistic_odeint(t[0], y0, r, K));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0c89f582",
   "metadata": {},
   "outputs": [],
   "source": [
    "# logistic_odeint = vmap(logistic_odeint, in_axes=(0, None, None, None))\n",
    "\n",
    "# plt.plot(t.T, logistic_odeint(t, y0, r, K).T);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "906c3fcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0004031221\n"
     ]
    }
   ],
   "source": [
    "def logistic_odeint_loss(params, t, y):\n",
    "    yhat = logistic_odeint(t, *params).reshape((1, -1))\n",
    "    return jnp.mean((yhat - y)**2)\n",
    "\n",
    "print(logistic_odeint_loss([y0, r, K], t[0], y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1f9e676a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "res = minimize(logistic_odeint_loss, params_guess, args=(t[0], y), method='BFGS')\n",
    "print(res.success)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1b3cdb72",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "if not res.success:\n",
    "    res = minimize(logistic_odeint_loss, res.x, args=(t[0], y), method='BFGS')\n",
    "    print(res.success)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7e9094b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2 0.5 1.2 | 0.0004031221\n",
      "[0.20128083 0.49919215 1.2042261 ] | 0.00038958865\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 552
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(y0, r, K, '|', logistic_odeint_loss([y0, r, K], t[0], y))\n",
    "print(res.x, '|', logistic_odeint_loss(res.x, t[0], y))\n",
    "\n",
    "plt.plot(t, y, '.k')\n",
    "plt.plot(t[0], logistic_odeint(t[0], *res.x), '-r');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2890b6e",
   "metadata": {},
   "source": [
    "### Fitting ODEnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "95fa2029",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mlp_ode(y, t, params):\n",
    "    y_and_t = jnp.hstack([y, t])\n",
    "    return mlp(params, y_and_t)\n",
    "\n",
    "def odenet_odeint(t, params):\n",
    "    return odeint(mlp_ode, y0, t, params)\n",
    "\n",
    "# odenet_odeint = vmap(odenet_odeint, in_axes=(0, None))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "59db54cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def odenet_loss(params, t, y):\n",
    "    yhat = odenet_odeint(t, params).reshape((1, -1))\n",
    "    return jnp.mean((yhat - y)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a1898b5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit\n",
    "def odenet_update(params, t, y):\n",
    "    grads = grad(odenet_loss)(params, t, y)\n",
    "    return [\n",
    "        (w - η * dw, b - η * db)\n",
    "        for (w, b), (dw, db) in zip(params, grads)\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "49301c0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "67\n"
     ]
    }
   ],
   "source": [
    "# We need to change the input dimension to 2, to allow time-dependent dynamics.\n",
    "odenet_layer_sizes = [2, 6, 6, 1] # t,y(t) -> ... -> y(t+dt)\n",
    "# Initialize \n",
    "odenet_params = init_random_params(param_scale, odenet_layer_sizes)\n",
    "print(sum(__.size for _ in odenet_params for __ in _))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3fbdd988",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 131.81291\n",
      "5000 0.0044554514\n",
      "10000 0.0023229162\n",
      "15000 0.0017886197\n",
      "20000 0.0014564791\n",
      "25000 0.001261144\n",
      "30000 0.0011124271\n",
      "35000 0.0009967838\n",
      "40000 0.0009056021\n",
      "45000 0.0008329434\n",
      "50000 0.0007745297\n",
      "55000 0.00072706793\n",
      "60000 0.000688042\n",
      "65000 0.00065569556\n",
      "70000 0.0006284404\n",
      "75000 0.0006052384\n",
      "80000 0.0005898033\n",
      "85000 0.0005779843\n",
      "90000 0.000567442\n",
      "95000 0.00055784016\n",
      "100000 0.0005489524\n",
      "105000 0.0005406805\n",
      "110000 0.00053310697\n",
      "115000 0.00052631256\n",
      "120000 0.0005199418\n",
      "125000 0.0005138974\n",
      "130000 0.0005082313\n",
      "135000 0.00050291576\n",
      "140000 0.000497857\n",
      "145000 0.00049304706\n",
      "150000 0.00048859866\n",
      "155000 0.0004845434\n",
      "160000 0.00048070843\n",
      "165000 0.000477074\n",
      "170000 0.0004735961\n",
      "175000 0.000470258\n",
      "180000 0.0004670442\n",
      "185000 0.00046400787\n",
      "190000 0.00046108747\n",
      "195000 0.00045828344\n",
      "200000 0.0004555908\n",
      "205000 0.00045304032\n",
      "210000 0.00045063236\n",
      "215000 0.00044832114\n",
      "220000 0.00044608646\n",
      "225000 0.00044407006\n",
      "230000 0.00044219842\n",
      "235000 0.00044043234\n",
      "240000 0.00043872616\n",
      "245000 0.00043710327\n",
      "250000 0.0004355227\n",
      "255000 0.00043401113\n",
      "260000 0.00043253863\n",
      "265000 0.00043111105\n",
      "270000 0.00042972778\n",
      "275000 0.00042839904\n",
      "280000 0.00042711833\n",
      "285000 0.00042588738\n",
      "290000 0.00042471252\n",
      "295000 0.0004235837\n",
      "300000 0.00042249475\n",
      "305000 0.00042144422\n",
      "310000 0.00042043335\n",
      "315000 0.00041946143\n",
      "320000 0.00041850653\n",
      "325000 0.0004175952\n",
      "330000 0.00041671604\n",
      "335000 0.00041587185\n",
      "340000 0.00041507528\n",
      "345000 0.0004143063\n",
      "350000 0.0004135817\n",
      "355000 0.00041288196\n",
      "360000 0.00041219706\n",
      "365000 0.00041152272\n",
      "370000 0.00041087248\n",
      "375000 0.00041026316\n",
      "380000 0.0004096793\n",
      "385000 0.00040911845\n",
      "390000 0.0004085675\n",
      "395000 0.0004080341\n",
      "400000 0.00040753031\n",
      "405000 0.00040706305\n",
      "410000 0.00040661887\n",
      "415000 0.00040618234\n",
      "420000 0.00040575973\n",
      "425000 0.00040534142\n",
      "430000 0.00040495928\n",
      "435000 0.0004045956\n",
      "440000 0.00040423733\n",
      "445000 0.00040389664\n",
      "450000 0.00040355587\n",
      "455000 0.0004032241\n",
      "460000 0.0004028958\n",
      "465000 0.00040257222\n",
      "470000 0.0004022519\n",
      "475000 0.00040194346\n",
      "480000 0.0004016443\n",
      "485000 0.00040136385\n",
      "490000 0.00040109124\n",
      "495000 0.0004008208\n",
      "500000 0.00040055448\n",
      "505000 0.00040029723\n",
      "510000 0.00040003966\n",
      "515000 0.00039979097\n",
      "520000 0.00039954597\n",
      "525000 0.00039930097\n",
      "530000 0.00039906503\n",
      "535000 0.00039883744\n",
      "540000 0.0003986405\n",
      "545000 0.00039845533\n",
      "550000 0.00039827317\n",
      "555000 0.00039809532\n",
      "560000 0.00039791677\n",
      "565000 0.00039774604\n",
      "570000 0.00039757046\n",
      "575000 0.00039739884\n",
      "580000 0.00039722773\n",
      "585000 0.0003970602\n",
      "590000 0.0003968896\n",
      "595000 0.00039672482\n",
      "600000 0.00039656038\n",
      "605000 0.00039639513\n",
      "610000 0.00039624234\n",
      "615000 0.0003960917\n",
      "620000 0.00039594478\n",
      "625000 0.00039579306\n",
      "630000 0.00039564815\n",
      "635000 0.00039550275\n",
      "640000 0.00039535842\n",
      "645000 0.00039521712\n",
      "650000 0.00039507277\n",
      "655000 0.00039493854\n",
      "660000 0.00039480077\n",
      "665000 0.00039466325\n",
      "670000 0.00039452498\n",
      "675000 0.00039438976\n",
      "680000 0.00039425638\n",
      "685000 0.00039412332\n",
      "690000 0.0003939876\n",
      "695000 0.00039385815\n",
      "700000 0.00039372992\n",
      "705000 0.0003936001\n",
      "710000 0.00039347247\n",
      "715000 0.00039334624\n",
      "720000 0.00039321993\n",
      "725000 0.0003931031\n",
      "730000 0.00039298754\n",
      "735000 0.00039287453\n",
      "740000 0.00039276117\n",
      "745000 0.0003926476\n",
      "750000 0.0003925359\n",
      "755000 0.00039242642\n",
      "760000 0.0003923155\n",
      "765000 0.00039220497\n",
      "770000 0.00039209434\n",
      "775000 0.00039198526\n",
      "780000 0.00039187877\n",
      "785000 0.00039176882\n",
      "790000 0.00039166294\n",
      "795000 0.00039155514\n",
      "800000 0.00039144678\n",
      "805000 0.00039134227\n",
      "810000 0.00039123622\n",
      "815000 0.00039113208\n",
      "820000 0.00039102524\n",
      "825000 0.0003909265\n",
      "830000 0.00039082926\n",
      "835000 0.0003907328\n",
      "840000 0.00039063595\n",
      "845000 0.0003905417\n",
      "850000 0.00039044925\n",
      "855000 0.000390357\n",
      "860000 0.00039026348\n",
      "865000 0.00039017072\n",
      "870000 0.00039007896\n",
      "875000 0.0003899867\n",
      "880000 0.0003898956\n",
      "885000 0.00038980338\n",
      "890000 0.00038971406\n",
      "895000 0.0003896256\n",
      "900000 0.00038953562\n",
      "905000 0.00038944578\n",
      "910000 0.00038935905\n",
      "915000 0.00038926926\n",
      "920000 0.00038917988\n",
      "925000 0.00038909324\n",
      "930000 0.00038900712\n",
      "935000 0.00038891908\n",
      "940000 0.00038882918\n",
      "945000 0.0003887425\n",
      "950000 0.00038865968\n",
      "955000 0.00038857406\n",
      "960000 0.00038849347\n",
      "965000 0.00038841218\n",
      "970000 0.00038832726\n",
      "975000 0.00038824376\n",
      "980000 0.00038816285\n",
      "985000 0.00038808427\n",
      "990000 0.00038799897\n",
      "995000 0.00038792053\n"
     ]
    }
   ],
   "source": [
    "# train\n",
    "η = 0.01\n",
    "train_iters = 1000000\n",
    "\n",
    "for i in range(train_iters):\n",
    "    odenet_params = odenet_update(odenet_params, t[0], y)\n",
    "    if i % 5000 == 0:\n",
    "        print(i, odenet_loss(odenet_params, t[0], y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c54ff630",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 525,
       "width": 1001
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 6))\n",
    "tt = jnp.linspace(t[0,0], t[0,-1], 500)\n",
    "\n",
    "ax = axes[0]\n",
    "ax.plot(t, y, '.k', markersize=2)\n",
    "yhat = odenet_odeint(tt, odenet_params).squeeze()\n",
    "ax.plot(tt, yhat, '-r', label='ODENet');\\\n",
    "ax.plot(tt, logistic(tt, y0, r, K), '-g', label='Logistic');\n",
    "ax.set_xlabel('$t$')\n",
    "ax.set_ylabel('$y$')\n",
    "ax.legend()\n",
    "\n",
    "ax = axes[1]\n",
    "dyhatdt = [mlp_ode(yhat[i], tt[i], odenet_params) for i in range(len(tt))]\n",
    "dydt = [logistic_ode(yhat[i], tt[i], r, K)  for i in range(len(tt))]\n",
    "\n",
    "ax.plot(yhat, dyhatdt, 'o', label='ODENet')\n",
    "ax.plot(yhat, dydt, 'o', label='Logistic')\n",
    "ax.set_ylim(0, max(dyhatdt))\n",
    "ax.set_xlabel('$y$')\n",
    "ax.set_ylabel('$dy/dt$')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3939d858",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:scipy]",
   "language": "python",
   "name": "conda-env-scipy-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}