learn_inflation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as jnp\n",
    "from jax import random, grad, jit, jacfwd, jacrev\n",
    "from jax.scipy.linalg import inv, svd, eigh, det\n",
    "from jax.lax import scan\n",
    "from scipy.linalg import solve_discrete_are, norm\n",
    "from tqdm.auto import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "from jax.tree_util import Partial\n",
    "from functools import partial\n",
    "from jax_vi import KL_gaussian, log_likelihood, KL_sum, plot_optimization_results\n",
    "from jax_filters import apply_filtering_fixed_nonlinear, kalman_filter_process, filter_step_nonlinear, ensrf_steps, kalman_filter_process\n",
    "from jax_models import visualize_observations, Lorenz96, KuramotoSivashinsky, generate_true_states, generate_localization_matrix\n",
    "\n",
    "# Parameters\n",
    "F = 8.0\n",
    "dt = 0.05\n",
    "num_steps = 250  # Number of time steps\n",
    "\n",
    "J0 = 0\n",
    "n = 40   # Number of state variables\n",
    "Q = 0.2 * jnp.eye(n)  # Process noise covariance\n",
    "R = 0.5 * jnp.eye(n)  # Observation noise covariance\n",
    "H = jnp.eye(n)  # Observation matrix\n",
    "\n",
    "N = 10 # number of MC samples\n",
    "n_ensemble = 30\n",
    "observation_interval = 1\n",
    "initial_state = random.normal(random.PRNGKey(0), (n,))  # Initial state\n",
    "m0 = initial_state\n",
    "C0 = Q\n",
    "\n",
    "l96_model = Lorenz96(dt = dt, F = F)\n",
    "l96_step = Partial(l96_model.step)\n",
    "state_transition_function = l96_step\n",
    "\n",
    "jacobian_function = jacrev(l96_step, argnums=0)\n",
    "jac_func = Partial(jacobian_function)\n",
    "# Generate true states and observations using the Lorenz '96 model\n",
    "key = random.PRNGKey(0)\n",
    "observations, true_states = generate_true_states(key, num_steps, n, initial_state, H, Q, R, l96_step, observation_interval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# plt.pcolormesh(c[-1])\n",
    "# plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from jax_vi import KL_gaussian, log_likelihood, KL_sum\n",
    "\n",
    "def var_cost(inflation, ensemble_init, observations, H, Q, R, localization_matrix, key, num_steps, J0):\n",
    "    pred_states, pred_covar, states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, inflation, key)\n",
    "    ensemble_mean = jnp.mean(states, axis=-1)  # Taking the mean across the ensemble members dimension\n",
    "    pred_mean = jnp.mean(pred_states, axis = -1)\n",
    "    key, *subkeys = random.split(key, num=N+1)\n",
    "    kl_sum = KL_sum(pred_mean, pred_covar, ensemble_mean, covariances, n, l96_step, Q, key)\n",
    "\n",
    "    def inner_map(subkey):\n",
    "        return log_likelihood(random.multivariate_normal(subkey, ensemble_mean, covariances), observations, H, R, num_steps, J0)  \n",
    "    cost = kl_sum - jnp.nanmean(jax.lax.map(inner_map, jnp.vstack(subkeys)))\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "base_m, base_C, base_K  = kalman_filter_process(l96_step, jac_func, m0, C0, observations, H, Q, R)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'var_cost' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[1], line 8\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m random\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mproperscoring\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m var_cost_grad \u001b[38;5;241m=\u001b[39m grad(var_cost, argnums\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n\u001b[1;32m     10\u001b[0m inflation_opt \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1.45\u001b[39m \u001b[38;5;66;03m# Example starting value for inflation\u001b[39;00m\n\u001b[1;32m     11\u001b[0m radius \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m16\u001b[39m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'var_cost' is not defined"
     ]
    }
   ],
   "source": [
    "from IPython.display import clear_output\n",
    "from jax import grad\n",
    "from tqdm.notebook import tqdm\n",
    "import jax.numpy as jnp\n",
    "from jax import random\n",
    "import properscoring\n",
    "\n",
    "var_cost_grad = grad(var_cost, argnums=0)\n",
    "\n",
    "inflation_opt = 1.45 # Example starting value for inflation\n",
    "radius = 16\n",
    "alpha = 1e-6  # Learning rate\n",
    "key = random.PRNGKey(0)  # Random key\n",
    "N = 20  # Number of MC samples\n",
    "m0 = initial_state\n",
    "C0 = Q  # Initial covariance, assuming Q is your process noise covariance\n",
    "localization_matrix = generate_localization_matrix(n, radius) \n",
    "ensemble_init = random.multivariate_normal(key, initial_state, Q, (n_ensemble,)).T\n",
    "\n",
    "crpss = []\n",
    "rmses=[]\n",
    "inflations = []\n",
    "true_div = []\n",
    "covars = []\n",
    "\n",
    "n_iters = 100\n",
    "\n",
    "\n",
    "for i in tqdm(range(n_iters)):\n",
    "    key, subkey = random.split(key)\n",
    "        \n",
    "    # Gradient descent step for inflation parameter\n",
    "    grad_inflation = var_cost_grad(inflation_opt, ensemble_init, observations, H, Q, R, localization_matrix, subkey, num_steps, J0)\n",
    "    inflation_opt -= alpha * grad_inflation  # Update inflation parameter\n",
    "    inflations.append(inflation_opt)\n",
    "\n",
    "    pred_states, pred_covariances, states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, inflation_opt, key)\n",
    "    ensemble_mean = jnp.mean(states, axis=-1)  # Taking the mean across the ensemble members dimension\n",
    "    rmse = jnp.sqrt(jnp.mean((ensemble_mean - true_states)**2))\n",
    "    rmses.append(rmse)\n",
    "    crps = properscoring.crps_ensemble(true_states, states).mean(axis=1).mean()\n",
    "    crpss.append(crps)\n",
    "    total_kl_divergence = 0\n",
    "    for t in range(num_steps):  \n",
    "        kl_div_t = KL_gaussian(n, ensemble_mean[t], covariances[t],  base_m[t], base_C[t])\n",
    "        total_kl_divergence += kl_div_t\n",
    "    true_div.append(total_kl_divergence / num_steps)\n",
    "    covars.append(covariances)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "@jit\n",
    "def resample_particles(key, particles, weights):\n",
    "    num_particles = particles.shape[0]\n",
    "    cumulative_sum = jnp.cumsum(weights)\n",
    "    indices = jnp.searchsorted(cumulative_sum, random.uniform(key, (num_particles,)))\n",
    "    return particles[indices]\n",
    "\n",
    "@jit\n",
    "def update_weights(particles, observation, H, R):\n",
    "    # Calculate the likelihood of each particle given the observation\n",
    "    predicted_observations = jax.vmap(lambda x: jnp.dot(H, x), in_axes=0, out_axes=0)(particles)\n",
    "    obs_dim = observation.shape[0]\n",
    "    inv_R = jnp.linalg.inv(R)\n",
    "    diff = observation - predicted_observations\n",
    "    likelihood = jnp.exp(-0.5 * jax.vmap(lambda d: jnp.dot(d, jnp.dot(inv_R, d.T)), in_axes=0, out_axes=0)(diff))\n",
    "    likelihood = likelihood / likelihood.sum()  # Normalize the weights\n",
    "    return likelihood\n",
    "\n",
    "@partial(jit, static_argnums=(1,2))\n",
    "def particle_filter(key, num_particles, num_steps, initial_state, observations, observation_interval, state_transition_function, H, Q, R):\n",
    "    mean = jnp.tile(initial_state, (num_particles, 1))\n",
    "    particles = random.multivariate_normal(key, mean, Q, shape=(num_particles,))\n",
    "    step = jax.vmap(state_transition_function, in_axes=0, out_axes=0)\n",
    "    ensemble = []\n",
    "    #for now we will assume observation_interval of 1\n",
    "    def body_fn(carry, t):\n",
    "        key, particles = carry\n",
    "        key, subkey = random.split(key)\n",
    "        # Transition particles to the next state\n",
    "        particles = step(particles) + random.multivariate_normal(subkey, jnp.zeros(particles.shape[1]), Q, shape=(num_particles,))\n",
    "        # Update weights and resample every step\n",
    "        observation = observations[t]\n",
    "        weights = update_weights(particles, observation, H, R)\n",
    "        particles = resample_particles(subkey, particles, weights)\n",
    "        return (key, particles), particles\n",
    "\n",
    "    keys_and_particles = jax.lax.scan(body_fn, (key, particles), jnp.arange(num_steps))\n",
    "    ensemble = keys_and_particles[1]\n",
    "    return jnp.transpose(ensemble, (0, 2, 1))\n",
    "    # Transpose to (timestep, state_dim, num_particles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from jax_filters import particle_filter\n",
    "# import jax_filters\n",
    "# import importlib\n",
    "# importlib.reload(jax_filters)\n",
    "num_particles = 20000\n",
    "estimated_states = particle_filter(key, num_particles, num_steps, initial_state, observations, observation_interval, state_transition_function, H, Q, R)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "covars[0].shape\n",
    "def calculate_covariance_matrix(states):\n",
    "    mean = jnp.mean(states, axis=2)\n",
    "    deviations = states - mean[:, :, jnp.newaxis]\n",
    "    covariance_matrix = jnp.einsum('ijk,ilk->ijl', deviations, deviations) / (states.shape[2] - 1)\n",
    "    return covariance_matrix\n",
    "particle_covars = calculate_covariance_matrix(estimated_states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "covar_diffs = []\n",
    "for iter_covars in covars:\n",
    "    frobenius_norms = jnp.array([jnp.linalg.norm(particle_covars[i] - iter_covars[i], 'fro') for i in range(num_steps)])\n",
    "    covar_diffs.append(jnp.mean(frobenius_norms))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f505ca886d0>]"
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(covar_diffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, (ax1, ax3) = plt.subplots(figsize=(10, 4), ncols=2)\n",
    "\n",
    "# Plotting the RMSE and CRPS on the primary y-axis\n",
    "color = 'tab:orange'\n",
    "ax1.set_xlabel('Iteration')\n",
    "ax1.set_ylabel('KL divergence to ExKF', color=color)\n",
    "ln1 = ax1.plot(range(1, n_iters+1), true_div, label='KL divergence to ExKF', color='tab:orange', linestyle='-')\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "# Create a twin y-axis for the inflation parameter\n",
    "ax2 = ax1.twinx()\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('Inflation', color=color)\n",
    "ln3 = ax2.plot(range(1, n_iters+1), inflations, label='Inflation', color=color, linestyle=':')\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "# Combine legends from both axes\n",
    "lns = ln1 + ln3\n",
    "labs = [l.get_label() for l in lns]\n",
    "ax1.legend(lns, labs, loc='upper right')\n",
    "\n",
    "ax3.plot(range(1, n_iters+1), rmses)\n",
    "ax3.set_xlabel(\"Iteration\")\n",
    "ax3.set_ylabel(\"Prediction error (RMSE)\")\n",
    "\n",
    "plt.tight_layout()\n",
    "#plt.title('Inflation Parameter and Divergence from True Solution over Iterations')\n",
    "#plt.show()\n",
    "plt.savefig(\"inflation_errors.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.pcolormesh(base_C[-1, :, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.pcolormesh(covariances[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ins = []\n",
    "cs = []\n",
    "ds = []\n",
    "\n",
    "for i in jnp.arange(1.0, 2.0, 0.01):\n",
    "    states, covariances = ensrf_steps(l96_step, ensemble_init, num_steps, observations, observation_interval, H, Q, R, localization_matrix, i, key)\n",
    "    ensemble_mean = jnp.mean(states, axis=-1)  # Taking the mean across the ensemble members dimension\n",
    "    total_kl_divergence = 0\n",
    "    for t in range(num_steps):  \n",
    "        kl_div_t = KL_gaussian(n, ensemble_mean[t], covariances[t],  m[t], C[t])\n",
    "        total_kl_divergence += kl_div_t/num_steps\n",
    "\n",
    "    c = var_cost(i, ensemble_init, observations, H, Q, R, localization_matrix, subkey, num_steps, J0)\n",
    "    print(i, c, total_kl_divergence)\n",
    "    cs.append(c)\n",
    "    ds.append(total_kl_divergence)\n",
    "    ins.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.plot(cs)\n",
    "plt.plot(jnp.array(ds)*300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.plot(ds[20:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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