{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5fbc2d16-59f9-4be3-b93e-1a5440c7efd0",
   "metadata": {},
   "source": [
    "# Tutorial 10 - Advanced Models for PDEs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1afe6a1e-3ab4-4f3f-ad47-f6cd66419504",
   "metadata": {},
   "source": [
    "In this tutorial we will be addressing a forward PDE problem using an architecture more advanced than the standard KAN used in Tutorial 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0a2ef2a6-f681-427f-8252-ade2111ce0e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from jaxkan.models.RGAKAN import RGAKAN\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "from jaxkan.pikan.pde import get_ac_res\n",
    "from jaxkan.pikan.sampling import get_collocs_grid\n",
    "from jaxkan.pikan.adaptive import (\n",
    "    apply_rba_weights,\n",
    "    get_causal_weights,\n",
    "    get_colloc_indices,\n",
    "    get_rad_indices,\n",
    "    lr_anneal,\n",
    "    update_rba_weights,\n",
    ")\n",
    "\n",
    "from typing import Union, List\n",
    "\n",
    "from flax import nnx\n",
    "import optax\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import os\n",
    "os.environ[\"TF_CPP_MIN_LOG_LEVEL\"] = \"3\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4144965f-84cf-4d9d-a95d-e98b4c9e6543",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "60e70a5d-0340-4bdc-af4e-150d0098a87e",
   "metadata": {},
   "source": [
    "## Data Generation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "166ad90d-430e-45ca-86a8-e6e4dbc1c943",
   "metadata": {},
   "source": [
    "We will once again be solving the Allen-Cahn Equation,\n",
    "\n",
    "$$ \\frac{\\partial u}{\\partial t} - D\\frac{\\partial^2 u}{\\partial x^2} + 5 \\left(u^3 - u\\right) = 0,$$\n",
    "\n",
    "for $D = 10^{-4}$ in the $\\Omega = [0,1]\\times [-1, 1]$ domain, subject to initial condition\n",
    "\n",
    "$$ u\\left(t=0, x\\right) = x^2 \\cos\\left(\\pi x\\right), $$\n",
    "\n",
    "and periodic boundary conditions\n",
    "\n",
    "$$ u\\left(t, x=-1\\right) = u\\left(t, x=1\\right). $$\n",
    "\n",
    "Again, we will be using adaptive training methods (see Tutorial 8 and [this](https://www.arxiv.org/abs/2510.23501) paper)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b986e75a-6d4a-402f-bea7-36d13f4a7866",
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 42\n",
    "\n",
    "# Generate Collocation points for PDE\n",
    "collocs_pool = get_collocs_grid(ranges=[(0, 1, 2**7), (-1, 1, 2**7)])\n",
    "\n",
    "# Generate Collocation points for IC\n",
    "ic_collocs = get_collocs_grid(ranges=[(0, 0, 1), (-1, 1, 2**6)])\n",
    "ic_data = ((ic_collocs[:,1]**2)*jnp.cos(jnp.pi*ic_collocs[:,1])).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0dbe48b2-a680-4043-a38c-fb18134229d1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "4e9d9bba-71e2-4d5b-95b1-36167fb70c1a",
   "metadata": {},
   "source": [
    "## RGA KAN Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd54c6c-3d28-4864-af38-3b22875d0f0a",
   "metadata": {},
   "source": [
    "Instead of using the vanilla KAN model, we will be using the Residual-Gated Adaptive Kolmogorv-Arnold Network introduced in [Training Deep Physics-Informed Kolmogorov-Arnold Networks](https://www.sciencedirect.com/science/article/pii/S0045782526000356). Once again, boundary conditions will be enforced directly via the model architecture, this time by applying periodical embeddings (see the API Reference of RGAKAN)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b350b56f-5daa-411f-9090-b544760c34ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize an RGA KAN model\n",
    "n_in = collocs_pool.shape[1]\n",
    "n_out = 1\n",
    "n_hidden = 8\n",
    "num_blocks = 2\n",
    "flavor = 'exact'\n",
    "D = 5\n",
    "init_scheme = {'type': 'glorot_fine'}\n",
    "alpha = 0.0\n",
    "beta = 0.0\n",
    "ref = None\n",
    "period_axes = {1 : (jnp.pi, False)}\n",
    "rff_std = None\n",
    "sine_D = 5\n",
    "\n",
    "model = RGAKAN(n_in = n_in, n_out = n_out, n_hidden = n_hidden, num_blocks = num_blocks, flavor = flavor, D = D,\n",
    "               init_scheme = init_scheme, alpha = alpha, beta = beta, ref = ref, period_axes = period_axes,\n",
    "               rff_std = rff_std, sine_D = sine_D, seed = seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0051714b-2f23-45c9-994f-90a6a0705da2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will also be using a more adaptive optimizer with learning rate scheduling\n",
    "lr_schedule = optax.exponential_decay(\n",
    "                init_value=1e-3,\n",
    "                transition_steps=1000,\n",
    "                decay_rate=0.9,\n",
    "                staircase=False\n",
    "            )\n",
    "\n",
    "opt_type = optax.adam(learning_rate=lr_schedule, b1=0.9, b2=0.999, eps=1e-8)\n",
    "\n",
    "optimizer = nnx.Optimizer(model, opt_type, wrt=nnx.Param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db825176-cba8-43e4-9488-dadd2d3b6672",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f681d135-c885-4e59-87d7-1ea16a157c50",
   "metadata": {},
   "source": [
    "## Adaptive Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4ee5f1a6-e853-4b76-9a6a-4e0d2375249e",
   "metadata": {},
   "outputs": [],
   "source": [
    "@nnx.jit\n",
    "def get_rad_collocs(model, pde_collocs_pool, sorted_indices, l_pde, l_pde_pool):\n",
    "    resids_pool = pde_res(model, pde_collocs_pool)\n",
    "    new_indices, new_pool, _ = get_rad_indices(\n",
    "        collocs_pool=pde_collocs_pool,\n",
    "        residuals=resids_pool,\n",
    "        old_indices=sorted_indices,\n",
    "        batch_weights=l_pde,\n",
    "        pool_weights=l_pde_pool,\n",
    "        batch_size=batch_size,\n",
    "        rad_a=rad_a,\n",
    "        rad_c=rad_c,\n",
    "        seed=seed,\n",
    "    )\n",
    "    return new_indices, new_pool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "65d77457-e41c-4e66-a15b-2b4f709eb022",
   "metadata": {},
   "outputs": [],
   "source": [
    "# PDE Residual\n",
    "pde_res = get_ac_res()\n",
    "\n",
    "# PDE Loss\n",
    "def pde_loss(model, l_E, collocs):\n",
    "\n",
    "    residuals = pde_res(model, collocs) # shape (batch_size, 1)\n",
    "\n",
    "    # Get new RBA weights\n",
    "    l_E_new = update_rba_weights(residuals, l_E, gamma=RBA_gamma, eta=RBA_eta)\n",
    "\n",
    "    # Multiply by RBA weights while keeping them out of the backward graph\n",
    "    w_resids = apply_rba_weights(residuals, l_E_new)\n",
    "\n",
    "    # Reshape residuals for causal training\n",
    "    residuals = w_resids.reshape(num_chunks, -1) # shape (num_chunks, points)\n",
    "\n",
    "    # Get average loss per chunk\n",
    "    loss = jnp.mean(residuals**2, axis=1)\n",
    "\n",
    "    # Get causal weights\n",
    "    weights = get_causal_weights(loss, M, causal_tol)\n",
    "\n",
    "    # Weighted loss\n",
    "    weighted_loss = jnp.mean(weights * loss)\n",
    "\n",
    "    return weighted_loss, l_E_new\n",
    "\n",
    "\n",
    "def ic_loss(model, l_I, ic_collocs, ic_data):\n",
    "\n",
    "    # Residual\n",
    "    ic_res = model(ic_collocs) - ic_data\n",
    "\n",
    "    # Get new RBA weights\n",
    "    l_I_new = update_rba_weights(ic_res, l_I, gamma=RBA_gamma, eta=RBA_eta)\n",
    "\n",
    "    # Multiply by RBA weights while keeping them out of the backward graph\n",
    "    w_resids = apply_rba_weights(ic_res, l_I_new)\n",
    "\n",
    "    # Loss\n",
    "    loss = jnp.mean(w_resids**2)\n",
    "\n",
    "    return loss, l_I_new\n",
    "\n",
    "\n",
    "@nnx.jit(static_argnames=(\"compute_grads_sep\",))\n",
    "def train_step(model, optimizer, collocs, ic_collocs, ic_data, λ_E, λ_I, l_E, l_I, compute_grads_sep=False):\n",
    "\n",
    "    def total_loss_fn(model):\n",
    "        (loss_E, l_E_new) = pde_loss(model, l_E, collocs)\n",
    "        (loss_I, l_I_new) = ic_loss(model, l_I, ic_collocs, ic_data)\n",
    "        total = λ_E * loss_E + λ_I * loss_I\n",
    "        return total, (loss_E, loss_I, l_E_new, l_I_new)\n",
    "\n",
    "    (loss, aux), grads = nnx.value_and_grad(total_loss_fn, has_aux=True)(model)\n",
    "\n",
    "    sep_grads = (None, None)\n",
    "    if compute_grads_sep:\n",
    "        grads_E = nnx.grad(lambda m: pde_loss(m, l_E, collocs)[0])(model)\n",
    "        grads_I = nnx.grad(lambda m: ic_loss(m, l_I, ic_collocs, ic_data)[0])(model)\n",
    "        sep_grads = (grads_E, grads_I)\n",
    "\n",
    "    optimizer.update(model, grads)\n",
    "\n",
    "    return loss, aux, sep_grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3196e686-4998-409b-94d2-c3dd3de3b98b",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 10_000\n",
    "\n",
    "# Define causal training parameters\n",
    "causal_tol = 1.0\n",
    "num_chunks = 32\n",
    "M = jnp.triu(jnp.ones((num_chunks, num_chunks)), k=1).T\n",
    "\n",
    "# Define LR Annealing parameters\n",
    "grad_mixing = 0.9\n",
    "f_grad_norm = 1000\n",
    "\n",
    "# Define resampling parameters\n",
    "batch_size = 2**12\n",
    "f_resample = 2000\n",
    "rad_a = 1.0\n",
    "rad_c = 1.0\n",
    "\n",
    "# Define RBA parameters\n",
    "RBA_gamma = 0.999\n",
    "RBA_eta = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "06e24b36-d5b3-4b75-9145-39aaf5743180",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize RBA weights - full pool\n",
    "l_E_pool = jnp.ones((collocs_pool.shape[0], 1))\n",
    "# Also get RBAs for ICs\n",
    "l_I = jnp.ones((ic_collocs.shape[0], 1))\n",
    "\n",
    "# Get starting collocation points & RBA weights\n",
    "sorted_indices = get_colloc_indices(collocs_pool=collocs_pool, batch_size=batch_size, px=None, seed=seed)\n",
    "\n",
    "pde_collocs = collocs_pool[sorted_indices]\n",
    "l_E = l_E_pool[sorted_indices]\n",
    "\n",
    "# Define global loss weights (initialization)\n",
    "λ_E = jnp.array(1.0, dtype=float)\n",
    "λ_I = jnp.array(1.0, dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d54a2ff-0795-40bd-92c9-32f28ad25d6e",
   "metadata": {},
   "source": [
    "Following this setup, we proceed to train the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c5459ff8-5e00-45b4-9e2a-95f1cd59cf7f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch No. 1000. Current loss: 1.46e-02. Performing learning-rate annealing.\n",
      "Epoch No. 2000. Current loss: 3.24e-02. Performing learning-rate annealing.\n",
      "Epoch No. 2000. Current loss: 3.24e-02. Performing RAD resampling.\n",
      "Epoch No. 3000. Current loss: 4.50e-02. Performing learning-rate annealing.\n",
      "Epoch No. 4000. Current loss: 1.05e-03. Performing learning-rate annealing.\n",
      "Epoch No. 4000. Current loss: 1.05e-03. Performing RAD resampling.\n",
      "Epoch No. 5000. Current loss: 8.24e-04. Performing learning-rate annealing.\n",
      "Epoch No. 6000. Current loss: 7.38e-04. Performing learning-rate annealing.\n",
      "Epoch No. 6000. Current loss: 7.38e-04. Performing RAD resampling.\n",
      "Epoch No. 7000. Current loss: 5.36e-04. Performing learning-rate annealing.\n",
      "Epoch No. 8000. Current loss: 6.69e-04. Performing learning-rate annealing.\n",
      "Epoch No. 8000. Current loss: 6.69e-04. Performing RAD resampling.\n",
      "Epoch No. 9000. Current loss: 5.53e-04. Performing learning-rate annealing.\n"
     ]
    }
   ],
   "source": [
    "train_losses = jnp.zeros((num_epochs,))\n",
    "\n",
    "# Start training\n",
    "for epoch in range(num_epochs):\n",
    "\n",
    "    do_anneal = (epoch != 0) and (epoch % f_grad_norm == 0)\n",
    "\n",
    "    loss, aux, sep_grads = train_step(\n",
    "        model, optimizer, pde_collocs, ic_collocs, ic_data, λ_E, λ_I, l_E, l_I,\n",
    "        compute_grads_sep=do_anneal\n",
    "    )\n",
    "\n",
    "    loss_E, loss_I, l_E, l_I = aux\n",
    "\n",
    "    # Perform lr annealing\n",
    "    if do_anneal:\n",
    "\n",
    "        print(f\"Epoch No. {epoch}. Current loss: {loss:.2e}. Performing learning-rate annealing.\")\n",
    "\n",
    "        λ_E, λ_I = lr_anneal((sep_grads[0], sep_grads[1]), (λ_E, λ_I), grad_mixing)\n",
    "\n",
    "    # Perform RAD\n",
    "    if (epoch != 0) and (epoch % f_resample == 0):\n",
    "\n",
    "        print(f\"Epoch No. {epoch}. Current loss: {loss:.2e}. Performing RAD resampling.\")\n",
    "\n",
    "        sorted_indices, l_E_pool = get_rad_collocs(\n",
    "            model, collocs_pool, sorted_indices, l_E, l_E_pool\n",
    "        )\n",
    "\n",
    "        # Set new batch of collocs and l_E\n",
    "        pde_collocs = collocs_pool[sorted_indices]\n",
    "        l_E = l_E_pool[sorted_indices]\n",
    "\n",
    "    # Append the loss\n",
    "    train_losses = train_losses.at[epoch].set(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d48ede2f-f25f-40fd-b472-5339e417c039",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "faab949e-dadb-4cec-bc13-63b10cb609c5",
   "metadata": {},
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b482774-013c-4f1a-98dc-6e3a44171783",
   "metadata": {},
   "source": [
    "By visualizing the train loss curve, we can see that even when training for a significantly smaller number of epochs than in the vanilla KAN case, the loss function decreases further."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8e82910c-d539-4ae1-adb4-c8d3caf597ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 4))\n",
    "\n",
    "plt.plot(np.array(train_losses), label='Train Loss', marker='o', color='#25599c', markersize=1)\n",
    "\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Training Loss Over Epochs')\n",
    "plt.yscale('log')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid(True, which='both', linestyle='--', linewidth=0.5) \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4860724c-a72f-41cf-8882-902e5c05f601",
   "metadata": {},
   "source": [
    "Additionally, the approximation to the actual solution is better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7798eb68-d6b5-47ec-b845-cf3d60dccf23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_t, N_x = 100, 256\n",
    "\n",
    "t = np.linspace(0.0, 1.0, N_t)\n",
    "x = np.linspace(-1.0, 1.0, N_x)\n",
    "T, X = np.meshgrid(t, x, indexing='ij')\n",
    "coords = np.stack([T.flatten(), X.flatten()], axis=1)\n",
    "\n",
    "output = model(jnp.array(coords))\n",
    "resplot = np.array(output).reshape(N_t, N_x)\n",
    "\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.pcolormesh(T, X, resplot, shading='auto', cmap='Spectral_r')\n",
    "plt.colorbar()\n",
    "\n",
    "plt.title('Solution of Allen-Cahn Equation')\n",
    "plt.xlabel('t')\n",
    "\n",
    "plt.ylabel('x')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88cc341a-8869-4dd9-be77-ef9bf2d8b5c1",
   "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": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}