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PINN in Pytensor with parameter recovery in PyMC
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "3d7c48ce", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import pymc as pm\n", | |
| "import pytensor\n", | |
| "import pytensor.tensor as pt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "id": "46aff230", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from pytensor_ml.layers import Linear, Sequential, Squeeze\n", | |
| "from pytensor_ml.activations import Tanh, Sigmoid\n", | |
| "from pytensor_ml.model import _xavier_normal_init\n", | |
| "\n", | |
| "import numpy as np\n", | |
| "from pymc.pytensorf import rewrite_pregrad" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "0d307154", | |
| "metadata": {}, | |
| "source": [ | |
| "# Heat Equation\n", | |
| "\n", | |
| "The classical 1d heat equation gives the heat on a homogenous rod at position $x$ at time $t$, $u(x,t)$, and follows the following PDE:\n", | |
| "\n", | |
| "$$\n", | |
| "\\begin{align}\n", | |
| "u_t &= \\alpha \\cdot u_{xx} \\\\\n", | |
| "u(0, x) &= u_0 \\\\\n", | |
| "u(t, x_{min}) &= 0 \\\\\n", | |
| "u(t, x_{max}) &= 0\n", | |
| "\\end{align}\n", | |
| "$$\n", | |
| "\n", | |
| "Boundary conditions are set so that the bar is in a vaccum (the temperature is zero beyond the ends of the bar), and we have an initial condition $u_0$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "d2036e18", | |
| "metadata": {}, | |
| "source": [ | |
| "# PINN\n", | |
| "\n", | |
| "Very simple network -- 4 layers with Tanh activations. I'm going to do everything in pytensor, because nobody ever does that :)\n", | |
| "\n", | |
| "Obviously you could do this in JAX or Pytorch instead. If you do, you will need to then wrap the network in a pytensor Op when you get to the PyMC step. See [here](https://www.pymc-labs.com/blog-posts/jax-functions-in-pymc-3-quick-examples) for examples of how this looks.\n", | |
| "\n", | |
| "Each of the four equations above is encoded into a component of the loss function. \n", | |
| "\n", | |
| "Note that we're implementing the core case only, so everything is a scalar." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "id": "3fe6c2c8", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "x_max = 1 # normalize rod to unit length\n", | |
| "\n", | |
| "alpha, t, u0, x = user_vars = pt.dscalars('alpha', 't', 'u0', 'x')\n", | |
| "inputs = pt.stack([alpha, t, x, u0])\n", | |
| "\n", | |
| "network = Sequential(\n", | |
| " Linear(name='embedding', n_in=4, n_out=32),\n", | |
| " Tanh(),\n", | |
| " Linear(name='layer_1', n_in=32, n_out=64),\n", | |
| " Tanh(),\n", | |
| " Linear(name='layer_2', n_in=64, n_out=64),\n", | |
| " Tanh(),\n", | |
| " Linear(name='layer_3', n_in=64, n_out=32),\n", | |
| " Tanh(),\n", | |
| " Linear(name='output', n_in=32, n_out=1),\n", | |
| " Squeeze\n", | |
| ")\n", | |
| "\n", | |
| "u = network(inputs)\n", | |
| "u = rewrite_pregrad(u)\n", | |
| "\n", | |
| "# Compute gradients u_t and u_xx\n", | |
| "du_x = pt.grad(u, x)\n", | |
| "du_x = rewrite_pregrad(du_x) \n", | |
| "\n", | |
| "du_xx = pt.grad(du_x, x)\n", | |
| "du_t = pt.grad(u, t)\n", | |
| "\n", | |
| "# Each part of the PDE (interior, initial condition, and boundary conditions) are given a term in the \n", | |
| "# loss function\n", | |
| "pde_loss = pt.square(du_t - alpha * du_xx)\n", | |
| "\n", | |
| "ic_loss = pt.square(network(pt.stack([alpha, 0.0, x, u0])) - u0) # initial condition\n", | |
| "boundary_loss_1 = pt.square(network(pt.stack([alpha, t, 0.0, u0])) - 0) # dirichlet condition\n", | |
| "boundary_loss_2 = pt.square(network(pt.stack([alpha, t, x_max, u0])) - 0) # dirichlet condition\n", | |
| "\n", | |
| "loss_terms = [pde_loss, ic_loss, boundary_loss_1, boundary_loss_2]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "157a7a4d", | |
| "metadata": {}, | |
| "source": [ | |
| "## Insert shared variables\n", | |
| "\n", | |
| "PyMC optimizers expect shared weights, so we need to swap out the symbolic weights for shared variables. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "id": "2344c0c2", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "rng = np.random.default_rng()\n", | |
| "\n", | |
| "weights = [weight for weight in pm.inputvars(loss_terms) if weight not in user_vars]\n", | |
| "\n", | |
| "shared_weights = [pytensor.shared(_xavier_normal_init(weight.type.shape, rng=rng, dtype='float64'), \n", | |
| " name=weight.name)\n", | |
| " for weight in weights]\n", | |
| "\n", | |
| "shared_replacements = dict(zip(weights, shared_weights))\n", | |
| "loss_terms = pytensor.graph_replace(loss_terms, shared_replacements, strict=False)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "c4cc037e", | |
| "metadata": {}, | |
| "source": [ | |
| "## Vectorize loss function\n", | |
| "\n", | |
| "As currently written, we will solve the PDE at a single point. That's a bit inefficient, so we can vectorize the graph so that its solved over a whole grid. We will solve over the same grid each time. You could also sample points on the grid. I don't know enough to know what is better." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "id": "8bcc336b", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Set up a grid, over (0, 1) x (0, 1)\n", | |
| "x_vec = np.linspace(0, x_max, 100)\n", | |
| "t_vec = np.linspace(0, 1, 100)\n", | |
| "\n", | |
| "xx, tt = np.meshgrid(x_vec, t_vec)\n", | |
| "xx = pt.as_tensor_variable(xx)\n", | |
| "tt = pt.as_tensor_variable(tt)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "id": "40f12628", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from pytensor.graph.replace import vectorize_graph\n", | |
| "\n", | |
| "# Vectorize the loss function, replacing x and t with the grids of values. \n", | |
| "# Also replace u0 with a vector of u0 values, so there is one initial value per point on the bar.\n", | |
| "u0_vec = pt.dvector('u0_vec')\n", | |
| "pde_loss, ic_loss, left_boundary, right_boundary = vectorize_graph(loss_terms, {x: xx, t: tt, u0:u0_vec})\n", | |
| "\n", | |
| "loss_mesh = pde_loss.mean() + ic_loss[0, :].mean() + left_boundary[:, 0].mean() + right_boundary[:, -1].mean()\n", | |
| "\n", | |
| "# Also vectorize the output function, so we can plot the results of training.\n", | |
| "out_mesh = vectorize_graph(pytensor.graph_replace(u, shared_replacements), {x: xx, t: tt, u0:u0_vec})" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "e0b3de21", | |
| "metadata": {}, | |
| "source": [ | |
| "## Optimizer\n", | |
| "\n", | |
| "The PyMC optimizers return symbolic updates, which we then pass to a training function.\n", | |
| "\n", | |
| "Do gradient clipping to a maximum L2-norm of 1.0 to stabilize training a bit" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "id": "76c2e4e8", | |
| "metadata": { | |
| "scrolled": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def norm_clip(w, max_norm=1.0, eps=1e-8):\n", | |
| " norm = pt.linalg.norm(w)\n", | |
| " scale = pt.switch(norm > max_norm,\n", | |
| " max_norm / (norm + eps),\n", | |
| " 1.0)\n", | |
| " return w * scale\n", | |
| "\n", | |
| "\n", | |
| "lr = pytensor.shared(1e-3, 'learning_rate')\n", | |
| "\n", | |
| "clipped_grads = [norm_clip(pt.grad(loss_mesh, weight)) for weight in shared_weights]\n", | |
| "updates = pm.adam(loss_or_grads=clipped_grads, \n", | |
| " params=shared_weights,\n", | |
| " learning_rate=lr)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "e31a61fe", | |
| "metadata": {}, | |
| "source": [ | |
| "## Compile\n", | |
| "\n", | |
| "One function for the training loop, and one function to make the plot." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "id": "c1bcea24", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "f_train = pytensor.function([alpha, u0_vec], loss_mesh, \n", | |
| " updates=updates, \n", | |
| " mode='JAX',\n", | |
| " trust_input=True)\n", | |
| "f_out = pytensor.function([alpha, u0_vec], out_mesh, trust_input=True, mode='JAX')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "ab7e1e88", | |
| "metadata": {}, | |
| "source": [ | |
| "# Train\n", | |
| "\n", | |
| "Simple training loop. Since we're using updates, pytensor will automatically handle the bookkeeping of the weights for us. \n", | |
| "\n", | |
| "The training history is pretty whack -- I don't claim to be an expert on fitting PINNs." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "id": "7aa20aef", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def lr_schedule(i, lr, reduce_lr=False, min_lr=1e-6):\n", | |
| " if i <= 1000:\n", | |
| " # Slowly go from 0 to 1e-3 over the first 1000 steps\n", | |
| " return i * (1e-3 / 1000)\n", | |
| " elif reduce_lr:\n", | |
| " # Otherwise, do a reduction if asked\n", | |
| " current_lr = lr.get_value()\n", | |
| " return max(current_lr / 2, min_lr)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "id": "48caa9d4", | |
| "metadata": { | |
| "scrolled": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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", | |
| "text/plain": [ | |
| "<Figure size 2016x576 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "from IPython.display import clear_output, display\n", | |
| "\n", | |
| "history = []\n", | |
| "\n", | |
| "patience = 500\n", | |
| "best_loss = float('inf')\n", | |
| "wait = 0\n", | |
| "threshold = 1e-4\n", | |
| "min_lr = 1e-6\n", | |
| "\n", | |
| "for i in range(4_000):\n", | |
| " lv = f_train(alpha=rng.beta(1, 1), u0_vec=np.abs(rng.normal(size=(100,))))\n", | |
| " loss_val = lv.mean().item()\n", | |
| " history.append(loss_val)\n", | |
| " \n", | |
| " if loss_val < best_loss - threshold:\n", | |
| " best_loss = loss_val\n", | |
| " wait = 0\n", | |
| " else:\n", | |
| " wait += 1\n", | |
| " \n", | |
| " reduce_flag = wait >= patience\n", | |
| " new_lr = lr_schedule(i, lr, reduce_flag)\n", | |
| "\n", | |
| " if i <= 1000 or reduce_flag:\n", | |
| " lr.set_value(new_lr)\n", | |
| " if reduce_flag:\n", | |
| " wait = 0\n", | |
| " \n", | |
| " if i % 25 == 0:\n", | |
| " clear_output(wait=True)\n", | |
| "\n", | |
| " fig, ax = plt.subplots(figsize=(14, 4), dpi=144, layout='constrained')\n", | |
| " ax.plot(history)\n", | |
| " plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "a1c9d3ac", | |
| "metadata": {}, | |
| "source": [ | |
| "## Plot results\n", | |
| "\n", | |
| "The plot looks about right, it's hot in the middle, and slowly cools down, radiating outwards from the hot point. Neat.\n", | |
| "\n", | |
| "The heat equation as we've set it up as a special case analytic solution as an infinite series of sine terms:\n", | |
| "\n", | |
| "$$\n", | |
| "u(x, t) = \\sum_{k=0}^\\infty \\left [ \\frac{4 u_0}{(2k + 1) \\pi} \\right ] \\sin \\left ( \\left ( 2k + 1 \\right ) \\pi x \\right ) \\exp \\left (-\\alpha \\left (2 k + 1 \\right )^2 \\pi^2 t \\right )\n", | |
| "$$\n", | |
| "\n", | |
| "We can check the PINN solution against this formula." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "id": "e2b4d713", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def analytic_solution(alpha, u0, x, t):\n", | |
| " k = pt.arange(1000)\n", | |
| " tk1_pi = (2 * k + 1) * np.pi\n", | |
| " term_1 = 4 * u0 / tk1_pi\n", | |
| " term_2 = pt.sin(tk1_pi * x)\n", | |
| " term_3 = pt.exp(-alpha * tk1_pi ** 2 * t)\n", | |
| " \n", | |
| " return (term_1 * term_2 * term_3).sum()\n", | |
| "\n", | |
| "analytic_solution_grid = vectorize_graph(analytic_solution(alpha, u0, x, t), {u0:u0_vec, x:xx, t:tt})\n", | |
| "fn_analytic = pytensor.function([alpha, u0_vec], analytic_solution_grid)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "id": "5e92761e", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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/dNa/Oy/v1ltvlSQtWbJk1IBIkqZOnaoDDzxQN910k+68804dcsghufff09Oj9c/36MHnHxn9g2rtg1GVakftDqoVv2OzfebqmjJXLzPPaWWu6UB/XF23T6XUs/3x84i2bqW2bsXUq5h9Vsy21YSyUHmH3PaDkdvG1auaeuG6cf1x/a64bU27rp4UODZ2+9rSlHohbvsiZIH3x9eN2z6pXqA7mXl/3Jnm6g24bc2FYdDW88dl0Jxtru5AZD3XH9/vHH2MrJu5skFXzzRitg1ckiSzT1vXlJnLQnS9cH/MdSV2n2Zbuz9bz18j3fbZ4MB2t39RG7Th+Y1+f01WyPjnhQ168PdPjP6B/ThEXvAVur/HXZ/9tmOvF2q73u3k60/s9u7DNPZtY8dTQ3XrO6bqsPXixipD27vxkykz27tt48djgfGhHT/Fved+nDX2cVJIEWOi0PiniLGOvTUEXnO9xzUDtp4Zg9hfoKSBuo9hYsdJtX1xYxUpMK6xv0zWFsWOS/KNf8beTnx/IreV7IAuqT8pbQTaCf5C8Fcvbt6gDT2bIzszWlMmhdauXStJmj9/vv35a1/7Wt10001at27dmAZFc+bM0YPPP6L9KoeOKq921/7VrTLFlHVPtvvNuifVlA12T6gpG+iufVv7J7uy2g98/yRzoZroP9z9td3RgN3e1DNlgxNrT7SB2penwYl+8J5NMCfqxNrBe8eE2u27JvTXlE3oqi2bPGFrbVlXbdkOXX22j1O6ttTW7aitu0Nnbb0pHXFlUzt6a8q6q7X1JGkHU+7quno7VGr7PalS+55NrNQegwn2t0nJnWoTzAioy9zUuiq153NXpXbStWpustXATb/D7LMIA5l/fwbNFXrQ3NW2ZrXv+Vazz61mf33mgr8lcA/oM4OGLVnte96b1V5/XsxqP9wvDtZeGDaZMlcvVHfDQO2FaqO5ALmyF/tNmbkobdxq6m01Fy9Jm7d21Zb11Zb1ba19z7b21ZYN9JlzdEvtMaj0+XO8uqV2e3NJUnVL7fbm8uPLemtPoM7ay9Rft3d1Tdnm2vO5c3Pt9adjU21ZdVPtC6xs8h3KNtUObrKNL9aUDb74t7K7spvtvlpBIeOf3z+ht77hU6PKs07zR60OU9YZmEyNrDvoyrrMLyIdZqxi6g0GRqm+HVPPlsVt68Y/5lL617rm3uDaNvXc2CnrMvcgM3aKHU9J8WOqHSaYMZEZU00x46SpXbWfYzdOkqQdzUXIjZ+mmLIdq7XXhakdtWVunBQcj5nx0yQzfnLjpElunOTGRKq9N7hxkuTHRUWMiULjn365cc3Yxzq9ZqzTayYUNgUuArHjmg2Dtb/TuTGMG6tsGKwtW9/fbfvjxjAbtpp9mnGNG8NsMmOYTWb80mvGKn1mrCL5Mcxgnzn/zLimsrX22FTNuKZq69nuBLavrWfHRKZedauZ2LX1fH863Pb9bp+RZWbbit2f/8xVBmrLK/2m7CX17vx/37b7itGUSaH169dLkqZNm2Z/Plz+wgsvbHc/CxcutOUPPPCAOuV/aQEAAGiGQsY/lelj7h8AACifpi5JHzIcc1SJfDQZAACg3TH+AQAARWvKk0LDfwkb/ovZtnp6ekbVC1mzZo0tX7hwoR781SP2ZwAAAM1QyPhn2zwhAACA7WjKpNCCBQskSevWrbM/f/DBByWFv3M/Vi/NHBixaVNNUaXTfBFcUqWr9u2qTqitW51Y+9W1CZNqyzJXNtlkFE32/RlwOUXdtd8N7Z9c+xdHm2dkopT8tv77z+bruBqYVFt3YHLt9yF7J9W+li2Tar+r3Dux9r3YNLH2y6G9E/2pvWXAfPe2q7aPW23A29gfrHPhiZLUYb573WW/o11b1me+6+4CrbsCIddOfM04A+Y746Ec93blXmOKPMfAhSX2mQdA+0yOwVbzfXxX1puZ77CbMik+P6jHXGx6Ir9n776jv7HP5CNt8ZlCW7bU9n3rltrXnfWaXKDe2ve2c7PJBOo1WRCBDJ9OkwfYudll+MTm+ph6m0y2m8n/GSqvvZ5WNpsMoN7aXI7MlGmLqddX28bgVt+frN98+b/4RVPrprDxz7bvkUsjdemWJsNb8iHFLnqk4oLT3T5dALCtFwhMNbdj146LYIktq5pTMnR9rrobmw2VNnlGNn3YZDiZem7brYGMmhSxAf3untQ/GBgzmnvVVpOJZ8s6XHZe7bX9RZfHaHJnJGmTzWmsvf7EZzfWlnXZcZvn8hydlK98uPM5NKZxH08To6Kt5hxwY+re2PzDQIahO96xGYguK2ijyxQyZS7rUPJ5hxtcVlC/ywqqb35Qv6knSYNbzdliMoAq/abM1bNltU24nCHJX7Pdddde2wdMXo+tZ9ow20qBBTQi92l/zYtdaCPwmXN1bdlLX0/C8KgpXx87+OCDJUk33XSTBrdZcWTDhg1auXKlJk+erLe+9a3N6B4AAEDdMf4BAACtpimTQq95zWu0ZMkSPfbYY/rWt7416mdnnHGGXnzxRX3sYx/TDjvUrgwGAADQjhj/AACAVtOUr49J0r/+67/qgAMO0IknnqhbbrlFe+65p+666y7ddtttmj9/vs4999xmdQ0AAKAhGP8AAIBW0rTVx17zmtfo3nvv1fLly3XXXXfp/PPP18MPP6wTTzxRq1ev1s4779ysrgEAADQE4x8AANBKmvakkCS9+tWv1ne+851mdsFz6YmSsgGTLOVCtlxAoNmfDZsybXRu9cmPVRMu1mFCVDs3m7DnSS5o2pRNMqGBpmxon3F1Bya68OnatgdMWPTWSbWvr88Ee280IdWS9JeJJiDQBFXvMLE2cHDKhNqyqV216bFTumqDDXfsNAGsknY0KbPTTNkUk1I7tVpbb0dTr7tighZN+KLkAxQnmUQ1VzbRpKy5oMSurLaNaiBQscMEWVbrPJc9aKIWBwJJbYMmDG6rqdtn6m0xu/RBi3Hhi5IPUNyUmWBnF6A4WBv27IIW19tQaJNKr2LColOCoiWpsqX2/KmaAOkO8xHp2GwCpE29ThMq3dHrz6lOU27LTKh0R68rM0GmvbXXuGqvD3bWFhMqvaV2+6yvtp5MgHRmAqTtvTRw3x2vGjr+yVSTIOuClG24pUszDtR1odI+WNPsb8CMnVwAdOC0cEGhmQl79uHTpo9u28hAakkyt057X8tM2y6E1b21mduf6dCgC7iWFPjE15ULn+7v9G9abCi1C5ruHay9D2zpMMG8VRNGXA0EBZtxkQ+aNmXV2rIJJprZBU13BMYbVXMcXd1qQrKsOwYDpkzyx9YtbOHDwse+iIU71lJg/GPLTIizKdvoxi9moYxQ0PSmfnOuRYZK9/ab9ychVNoGSkuSKa/0mzJzTXLXKRcKXXUh1YGLT3SotG0nblt3r7CLHygQXh0b9hx574ttQ5JfIMLet19aNvbrQdOeFAIAAAAAAEDzMCkEAAAAAABQQkwKAQAAAAAAlBCTQgAAAAAAACXU1KDpVpUFAp8qLrzPBGZm/bXpVy7EUCY00MW7hSKj7IyeC2W04Ve1QXA2oMsEhlUDAWYDJne0asoGJppguz4XSG22NYGwgxNNSLUJ0pakvglx4dWbJ5iwXhNIPWlCbeDuDhNq63V3mTdCPpR6qiszybVTTMKtK5vqwqcDQdMugNrVrXfQYlcgTdSHKtY3LjNP0KIPUKwt61NcMKYLVXRBiS5QMVR3gwmLdmGJrmxDvwmkNkHRLjxa8gGKL/aZ123K+kyA9EBf7fvoAqQr5vrRaa4VkuRO/Y4tcQHS5qOkDpMgboOmXdK4pM4tLizaBIxucQHSrswEufeZz4wJlJZ8qLS2mjJzn3P3PnePdPek0H0XY1PZJowyG3SJl+YzYoKQJdnkYxfY7PLCbSC1GU/ZUM5A0LTbpwsUdeMsO3hy4zu3bSCH25W7l101bdu3x4WoukVMzBuUmfuPJHM3TuOChzNT5uqFyrd21vZ9y2DtuG1Lpykz9bo7au9J3W5gKulFE0AdO9aZNFhb1mUO4gQz/qnagbvUYY6tHROFPiTbGMzingMIjX8GzPZbzbnmQqX7IsPCezOzuEQgaNotwLHJjGtcqPTmgdp9ugDpFwdcKLTvz2ZT/qIZE20xodJb+s04MiFUOuvzx7rigqYjQ6Vjf0e0odCBi48Pqnbbx4VFu3ZscHXo93wbDB1bLzJA2gZF2+7Y25K9XLh9jgFPCgEAAAAAAJQQk0IAAAAAAAAlxKQQAAAAAABACTEpBAAAAAAAUEJMCgEAAAAAAJQQq4+5xO7Q6hJmWQ230kLFrfLhVimrmlV0TGx7pcPP3WVmVQRbM3bqz4WXu9UKQinpbnUSV2bT4U36vU2lNytFmYVxgiuk1S4EoEGzclH/hNpj0z/RrIox0awe1VX7Aid0+RWzJpuVyiZ31ZbtYFYv6+6sLdvBlE3uMPtzSytJ6u6o3X6iOSfd6hsT3Yoc5hx1K3J02Ih9X9dxK3I4oVU1tuVWz5CkAbdaiqnrVhVzK2i41Te22BU1zIkr6UWz0oZfVaN2+02mzK2UsXmrWZ3PrB4mSX1mZYytW2s/NwNbzOo4psytKtaxpfazbU5bVc2KYqG67uPgVykzK42ZMlevo8+fox29ZoUZsyJZ1a0+ZlYVsyuN9dV+Div9geVA3KpiA3H3NJl7X2ZX2ohbLeevO4ivi7/Kat83u3qY2TJ4fzc/cCuwuBW73GpzZkVWOzYIjF9iVyqLXk3GrQBm2g72x9W1q4qZ123uf1W3sbnPDZp6oU9MZjqZsiKZHTKae2T/YGA8ZsaX/WaVqn5br7asryNuRbJNVX8/teMfu9JY7TXSjVX8SqvNG/84bkwUWqVswPwyYVdfNWOY2JVbY8dJkl9VzB1vNyZyZW5M1Ou2Daw+1mtWFes1Y6I+U8+Nk5JWGjPXGcmvNGbL3Mperl7kSmOhU9mushi50pgvM9fSyFXKJKnaH7eCWHRZ5IpkFTfGkuyYatuVRYfqveS/E4ZMPCkEAAAAAABQQkwKAQAAAAAAlBCTQgAAAAAAACXEpBAAAAAAAEAJETTtBEMwTTiq3d6FQLkyEz7twiADgaAu0DGr1s7zuRAxG2LocsnicnmHqgbCBGu4bG+XY2oDIuMC0QZDIWsm1Gywv7bfg1tNoKN5H11g7sCE2o73TfAftd6u2sC6jSaoen1nbccnmvDqSa5eh6lnyoa2N8HXJqh6gkkB7zIH0YU0dlZNsK5LLJXUFUqD20Y1MlltMDZoetB/1l3QogvRdGGJW10wZmQoYm8o2HDABGuaMheAuCUpANG/P4N9ptyEINprkgmVji2zQdEmgD5Y14RAu3ouLNqVdfaasMM+f453mPJqnwmV3lpbVjFlMvcLew8J3Fcyt1CCuVfZe1pKKHSe8Gm8vG2OhQundCHgocBLF1Lsw6tNOzYA2o1BXCin7U4gLDouxNnXM/szr8UHQCt+/GTLTNiv67fZ2OR1B+6m/hi6T6y7MvhQaVfmgosD/TFl7n7qyvo6TEixC5o2ZW5MJPmQYjdesQttuKBpM05yodAukFqSqubkD42VxsqNaUJcMLQLpY4NlXYB0j582o+f3VgpZUzlxlOu3pYBP/5JGVMN9Jv31oVKu0V0XHh9YLEdGwztytwCPjYUOq6NwCnuA60jt69GhkrHhkIH69rga3fxMzu0F0nTbmjo5D7uLxM+nePX9ho8KQQAAAAAAFBCTAoBAAAAAACUEJNCAAAAAAAAJcSkEAAAAAAAQAkRNJ3KhVWZcDgb6GjDp03ZQCChq8PM6Zm6LtTVBRv68Ok8SdO1dd0J5gK1fJkJdraBYaZeKNTMZaiakLZBE7LmgqYHu+ICqQdN2K4k9XWaQL6u2k66QOrOztoX2dlZu21XR229LrOtJE1wdU3ZBJPm1mECGV1IY6dJjHP1JKlqTozYUOlYLnx60Jx7UiAE0wQjunoDLizTBFpvNSGGfYFgw60mnNBt32/C1PuTgg0DIYaxAdK2Xu3+bD0XgGi27TBlQ3VdWLTbPi5UumOLOUdNUL0LlB7qjwma3mqCBGODpt3Fz4VHhy6Skfcld0+z7YRSZtE4mWoDKt1H1o1LAtc+d7j9GMbUc+MId065AOjQvdwNVyLHB24c4MpcaKkLgJakikl8jh1SuTI/HjPjjcjQ7KEf1BZl5sRwr9BdvVxcswuadmWh8oHOuHvnVjN26hus7ZG7x04IXPs2d9SOs9yiGhOrtfVcWLQb17h6HYE0dTfWcXXrvdDGgAmPDm3vFuVIWZDDhUr3B/pjg6bN+KfX1HMLcmwxodBufy5QWpL6B8x5mhAqrYRQ6dBCG1W3vQt2jqxnQ6ojyyQfFu1DpWvLbMh15P5C9xV7/3L7jA2ktvXcOMlfA9wCEfZinLLIx0vwpBAAAAAAAEAJMSkEAAAAAABQQkwKAQAAAAAAlBCTQgAAAAAAACVE0HQOmQuM8vmvtVyIVObCpkz6VSBkTSasqmKC7TJTVum3aVq1RTmyp20wYuy8o8vIssGWkeHTgRCxgYH6hqxVavPrbDjuYKcPARvsMiGPJmh6oKN2+4FOE4pngqarpu2qCY+WpA7TTkdH7T5dqLQvM/tz52MgvNMFTeeIPo9iQzXzBGPaUOnYeqbMhBW681aSBk0IogtOz1wwtKkn9/lIDTF0wdCxAdKRZS4AOtRHFyrtg6Hjyty2Ljy6YsKjh8rjAqTtNdvdA1yIoSsLBRPae1B8MGIMdy9Fg9nAyrgw46FiFzZuKrpgZ3MfcKeUC2sOBZX7sGhzXXG3Oruyhblv5xj/VMwl1gdIu41ri1zbVXv3c+9P4H5hS90ezbjE3PvsfbLLBU0H2nHrqrh7ogufNm27MGO38MLETp9660KpO02otAuf7jInZKc5+Vy9aiho2pynHdFHcexcULTkj7dbaMMdmz4TIO1Cql2odGihDbdPFyDtzoEtbkGPyIU7tgaCpgfMOMuVDbrxWJ1Dpd1YbGh7U9eNx1xYtAuAjgyVdiHMUuD3qtgA6cgFA2JDoYN1IxdZiC6LTfKXAotBmB0QNA0AAAAAAICxYlIIAAAAAACghJgUAgAAAAAAKCEmhQAAAAAAAEqIoOlUJi3RBfLZYCgXoGgSqDIXEiqp4tK4Omrn+Sr9tfWyyATpiimr2qTEPMxcZNxbYfNSXbBYKJjXhYu5YN5BE35my1yotAufDnzSXN2sw4QHm7DozJaZoDvzdg90+A5tNUHTFRM0XXH1TJioC0p0BzYY3pmj7lj5zLZQ0LQrjAvgzExyaGbO08wesMCLduXuM2KD0124oKnnwgUDIc52nzYEMW6fviwuVLrD1MtTt+pCpfvjQqWrfbVvWtUFRSsQQO3qmuu4u7bbAOgBcw8I3FfsfcmV2eBhV6/xwagYraLaMYc7NNHh0VJgvGKuF/b8cZvGhUrbsYoCYaTuz5zuHuLCsF2QqR0T2e4E7nVjD6+Ovc/5PgaufSaAOjp82n20zVjO5bdmZpwz9AO3KEdtj9z91C3msNWMnbaaRTVcoLQkTTADtS6zfadZYcSFSneaRTU6cwRNd5jjWLXB4vU1GAgq9+HeZrxqtnch4C4o2oaFB46XDYF27fSbdsw4y+2v34ZH+/64UGm7yIf5vSFlkY/YhXEkP8bzwdCuncgycxGwgf+B8mrk9r5e3MJDgY9cINA67p7mF3NwZeZ3qjxp/C/XTkLoNE8KAQAAAAAAlBCTQgAAAAAAACXEpBAAAAAAAEAJMSkEAAAAAABQQgRNN5EL5ay4UM5QUGfmAmltoqOpZ0JLXYC0mzYMhMwmzTDaYN/YQOrIsEv5cEJX1waTmSA4FyBtA6k7fXCfC43LTIadyeNTZvbpTonMhEK7NsJ1TXheZKCnzUc2gdSBXENfHgjRHDN37oWacOUuOTQykNoGsLrAwWBweuT2Nny6tiw2aDocYhhXZtt2Yc+RgdQ2KDrURxtU7cpMIKgNpI4Lla5s9UmLFXctNmXumu1Dpd09JEcAtF08ofHhpqizbY+ZTTh2gZWBa42ra67l9lRx9127koRr13bH3htseKgLYo4NlTb7CwWm2rfXvD928Q57nzNtmGp+3Q//pg2aG1N0+LQNmnb1agcHLiha8mMYV3fQvLluTNVvroduzOfCjCVpa7V2YNRprqcufLrDBkjXvkMufDoUHu0CqG2geZ2FjtegO7aRodIDpqzf7M+FPbuA61Dd2ADpAVPPhUoPmm3d4jRSIFTahkDH1YsNlfbjpMB1PDJUOnosZ8egce3m2t4GQEdu637HC/yOaPcZub0ts/dDUxYaY8XWrdMYjSeFAAAAAAAASohJIQAAAAAAgBJiUggAAAAAAKCEmBQCAAAAAAAoIYKmG8EFWNn0KpdM6EKhfSBoZvZZsSlbLuTRhBSbbV29cPJjrdhZx4oJnHMBXTZU2gZNB0LWzFs56DJdu0yYmwk6cwHQFROAaPILg9tnpqxq0iSjA6lt+LTvTxYZNp65gFEbPh3Xn2B4dPypVl/BoOm4MFIbiG4D7CLDpwOZwD5ULy6I0G9ryiIDB0P7rPbHhUC7dmIDpH0bgfDOhKDpigufjgyVrph6wfJ+Fz4dGSptAqmz2G0lf/9ygda2jEDqlrFN8GTFBFG6bEpXL1TXj3UiF35w9xV7f7fdCYT0m3pmB/Gh0uaeHxj/2O3tdTJun64Zd3u24dOuWSk+vDo2fNqw50ngGGY2lNrUM/c0VzbQUdvLwU4TKBy49nWYEOhOs88OEz7cERkq7QLWXT0pHEAds89Y7jPnwqOlQAi4KXOh0q5edCC1CYWWfAC1D5A2YdGm3qBZpGPQhUIHFv6QqeuCoX1Z7e7swh8J9SQflB87HksZ34UC+t011o+VXX8iw55dPVMW2l6urrvQRY6d7D02cN+txI6zCJoGAAAAAADAWDEpBAAAAAAAUEJMCgEAAAAAAJQQk0IAAAAAAAAlxKQQAAAAAABACbH6WB6ZWyEgsIzTtpuaZHC/GoirF1j3wZS7FRl8ermpZxL1o1ckCzF13Uxk/AoapjR2FRLFrwDlEugHXcK/Wyms02wbOE2qZqUyV9etFubK3CpnbkUxuwJYqNyuPha5bfTqY/HnVL3XN8q1wFnkqmKFrT4WvUrD2MvcqhGV0Mpetq6pZ1enSFhpzKweFu5jnVcaSyiTFL/SWOQKYJmr5+4hgfuKuwe5lS1svVihexqK5Q5DaCUjd5901/LIVc7s/lzbgXu5WXjIXyfNuMau7BW50lhw1Rq7oqupF7dAbNI4KfTpcn10K1zFrkjmF+BxN/3QinbmXHErjXXGjXWrbnUsU6+jIzC6NKuA9ZvrqVtpzG3bYVZprdrV8AL3KlfX1qyv4IJ/5v11q5e5FcQG3GpxkauUuRXFJH9s3apibvvM/b7j2jHj/tDqY/ErjbnVjd3+asvsSmNbTb3Q70DRq4q5MreKV9z+wqt9mXbcGM2uIGZ2mLBKWbCuHc9H7tP+fhBZrwl4UggAAAAAAKCEmBQCAAAAAAAoISaFAAAAAAAASohJIQAAAAAAgBIiaDpR5sKmTOBcbCC1DRMNhfC6MFKX/DgQmWzoylwQrglGldIC8CLzKn2Ab4cJmwskKftwsLjQbRsqbd6KQbdt4PBnLjTX1B00r9Fmbrt2YusF6tpQaXv+uHqmjdiy0PZObL3IbNxQ1qrd3p2TCfVsWGoghM6GCdrgvth6Yw8SDLUTG05oA6RtKHTk/kxQ9FDdyKBpc321AdJbTVC0C5UOXDdjA6Tt9d5d213YoQ2uDgUKJyQe2sUP6h0Nj5eVZbXH115sEmNrYwMzXWCzOy9ypCbba5C9L7l7fty2NnQ08J65a5Xbpw1xNn20IdeR987QYXXhsYNmB7Hh0+4GXbVB46EbvCmy904TFOwWA3Eh1W58GLgmVc34eaDDLDjgAqRNmQuQdsfalYW2D4VSj1Xw2ETWHYgMn7ah0C5oOjI8OtiODZCODIvuj1zIxoVPB8ptMHRKqLRdpCNuf0P7jCuz177IhUh8ULTvT2w7tiwy7Dl2MZihcpueH1cWuaBUdL1Qf2LLxoAnhQAAAAAAAEqISSEAAAAAAIASYlIIAAAAAACghJgUAgAAAAAAKCGCpp1QYFNKKKMLpXLpVx21CcBZoD8VE+ppgz5NGFslMnzahSrmibOKfsciw718ILVLOA400xlX1wVDu8OVuXoueC0Q7OwCpF2wc7XDhDeafVYjg6KrVX9kbKi0e9Pd2xhbL0fQtJWYjVojzwmdEiodGXbn6tltFR+qZ8uiw/xqy2yoamD72PBqH0htrgGung2pDgRNu+1dWHRs0HRsqLS75gbaiQ2VtveG6PtCjhPfhmHXOUC6TkGJ+Ktt38/IcMvg8CeybsXejyPbiQ2PViiQ37RjA6TdDuNCpUOBqW5NDns9dS/H1nPjn8jgalOWp27smCrrdIHU8eMxW+4uX7aeGTu5428XEvEdykyotAtDtgHQZoEZHz5d224oPDo2VDrlV5M8l93YAGlXzx2Hwch6rkzKESDtyiIXmHHbumBmyQdN27FXAaHSoT7aUGk3frLh0wllORZLSQmQtsHV7t4XGsO6dtz2Nnza7DB2MYbQBzE20Pql9RKGUjwpBAAAAAAAUEJMCgEAAAAAAJQQk0IAAAAAAAAlxKQQAAAAAABACRE03UQu6NMFWgW5AKpAuGptQy54zQWmmk0Du3SBjnm2HzOTcGwy/4aqugBFF2xnAqBdCJ2tZz5VLhRa8sHQg6auD4COC6l2bWehAMPIoOnYsGjXRytQzbZTgGC+Y+TH04bQRYZU+wDVQDtu+8iQv9jgvtggwFDbsQHSsWU2uNq2EQqaNmHR9Q6VNtfSUH9it7dBhC682rWTJxTahgITAt327GIXLgQzcNGNrWvruf2Ze6cNnw4lX7u6Uc0EtnULbbhtQ9c+E0hrL/qRYdFuqGL2V43c31B/3D4N022/rXnN7voR6I8PJDbtuIGAW3zDnj9u3BYImnZBwy4s2paZ42AX3zDb2t4EgqYjw6ej5Rhk2ePl6sWGRbth0oAbFAc65PYZHSBdW+Tq2fGUCYWWAuMnG+wc105KqHQwDNuOqVy9uP7Y8VhkAPRQ3biFSPxxMOOs6LFuaDUi13Zk2LNd+GPs9YLlL1s29msETwoBAAAAAACUEJNCAAAAAAAAJcSkEAAAAAAAQAkxKQQAAAAAAFBCBE23GhcwatMOpcykFFdcSp8Lh3PBqq6R2EBq+QC0zJ1hKeHT7u1xuZahbEoXQtdpAgJNQmBmwsayTnMMXD0TSD1UbkLfXGBhdPh0XFkw2NmFV9sA6bh92kDrPOHRTQqazpXTFpsFGRkq7cOnc4Ti2aC9uH3Ghkq70L+h8sjQwciAwKoNgI77wFddKLQk2bbrHCodGx4tRQdIu2u2DxysrWeDokP9CZWjvWx7zN29PMdiF67Y1fX14tq2TQfv5aaqC692IaHuvXABwJEB2UPFce3YoFdzo3MZujbs2bTr9pdrn5HjNretCyMeDIWounbM9ja82r0YFygcG0gt+WNrQqUzW+b2Z86pHOHl7jDa86zO7IIsUiBVeuyh0j4oOq4NKRAgbUOOIwOkXT27P9ud+ABp9ztQbNhz9Lb+PInd3odPx40FY8OnJf97ox9HRo4t7QJM8cHOdkEQO34yG9sFRiLbDo7xc4Rk1wFPCgEAAAAAAJQQk0IAAAAAAAAlxKQQAAAAAABACTEpBAAAAAAAUEIETadyoZ4mpLhSNalUpp5cIHEwFc9wAVQ+udY040LSAolqkeoePm1CA93744IJJR+k7BICXVCaC5XOTLCYDXs220pSZt5et30lIWjaBkC790E+GDo+VDq2Xo706DYImrbBrAWETw/VjWw7MpDPBhZGBvxJ8QHSdp922/rWkxQfBljvUGkXYCj5UOnIAGl7vY8NIUy9r9h7X2S/UTx7vHOMN1worF3lIbae644Zg4TyN+2aHJGh0uY89SHVpuFAh2xYtLkYV2JDrl2Irm23lmt3qK4LgY7bZ2bGIPaT7fYXCAp21znXjhub2jVVXKh0bJixZF+4Hf8Exk+19dx5ZurlCJq2NWPHSbGX/FA9GxgfuX3ktm4xmNDxqnvQdGSodDXw2bT7dL/buEU1YgOgI4OZXb3kfcaGSts2AsHOdnzp9hm3KEJ8SHWgP67Y7tONx8y2diwXH3wdPU7LM57bDp4UAgAAAAAAKCEmhQAAAAAAAEqISSEAAAAAAIASYlIIAAAAAACghAiabjEueM8GWkk2QDGrmpBrm8hngtJc4Klr1vcmWlL4tEn9s8HMocZNkLcLFstMPReimnWY/tht/TG0YdEubLzfHWsXCu1CLF0bgSBuG4Lp6pmN612vBfmwaBeA5+rF7s/VC4TiuSBUG94YGRYdHdxnuxMfEGhCl2O3jQ+K9p2011MXAl3vUOlAaL+9Nri6keHTNqTahiIGrkl1CixEk217HCMDl+1iF/LXIHeqRNezp585n0N/u4zMs3bhn+5+Y9c/cGXmXixJ6owLlXZhre6tqJoL+WDk6Cu8loMJj7UB2VGbBkKu47YdKo8NLo5t3Izv3BgrcP+KDpV2J5pdkCNu3LadA9ZaoscrkWHR7nhFfoalQIC0XdjCbRtbLzKAPlDuPu+27TqHSufpY2yodOxYMFews33Pxx4WHbv4SnBBDjfuiwyGjq3nF+6ID+KuV6i0w5NCAAAAAAAAJcSkEAAAAAAAQAkxKQQAAAAAAFBCTAoBAAAAAACUEJNCAAAAAAAAJcTqY+0sdpUZu7KBiZbv6DD7i10yScHVdWLYFcncClku8T2yniS72kFmXrZdPcGtQuHeHrdwkNtWsiu9ZGa1A7e9XbjDrRzjVsAw77ckya1oFrsiWewUszl/bBstyK8uELmtXe0rso3Q6huxq6G51RyiVykzFd1qX6G69jMSt/qYa6dirjOxq5QN7TNypbHIetErjQWvSZHXL7dPt63rIyuKwS4B5i7kgXPFrl7m6rlz0t1P3TUpR3/cae7qmX77lc9iV4UKjX9MO3ZFs7hVypzYFcny3U4TViQz3OJabowlBRZUtIssunGbW301sm13PiqwUlnCKq++LHbZvBz7TJHn1mDHG2NfQcyPiWI/r/Erjbm2q5GrisWuUpZr++hVysa+0lho9bFq7ApiCSuSVftzjGGjV8Y1ZW7cZ8e/keNNyfczdkyestJYnjFa6vbbwZNCAAAAAAAAJcSkEAAAAAAAQAkxKQQAAAAAAFBCTAoBAAAAAACUEEHTecQGNbpNXZhW1QWZ1s7ThQJ8Ky5Q1IRFZy54KzYg0lTMAgFmlQ6X0ucCU+MiC3NEPEazQZY2mM4FY9a+PhdW5kIIK4GgaReg6AKtXRClDZU2wWuxQdGhfWahEMSafcaFYfu2cxzZZgYtRm4fGwDt2I9hINg5Oqg6dp/2WhEZPi3ZUL3oAGkb4hxZL891pt6h0pGhf1moP5lrOy6w0F3bLfNagtvaYESzfegciEHwdWNltZ87e7/IEWpvA5Jd05HXJHvvsyHVof5EBtyGrp0R+7OfucCYLzow1bxrsQHStsgNIQJjtOhccHO8quZmHpt3GrxUuBBoV9eNgV0gsRuC2jGa744rd2O32HGNq1exN/jA+LDFgqb9uMaVRYZFR46dQsHOsQHSsSHXsaHS4RDnyH3GBjYnBVcHFgOJDbm275kLcTaN2OMS6k/kmDO2nivLMR7342e3z4Sw58hxdq59vnT7hOFV8pNCzz33nC655BIdeeSRmjdvniZPnqxp06bpbW97my699FINBlaAWbVqlQ4//HDNmDFD3d3d2muvvXTBBRdoIGEFKwAAgCIw/gEAAONB8pNCV155pT7zmc9o1qxZOvjgg7XHHnvoqaee0n/+53/q+OOP189//nNdeeWVo550uPbaa3XUUUdp0qRJOvbYYzVjxgz95Cc/0SmnnKKVK1fqyiuvTO0WAABAwzD+AQAA40Eli37+3Lv11lv14osv6j3veY+qL/l6zZNPPql9991Xf/zjH3XVVVfpqKOOkiT19PRo3rx5Wr9+vVauXKl99tlHktTb26vFixdr9erVuvzyy7Vs2bIx92nhwoV68FePaL/KoSkvLY79ak7cA1j2K0Vu28BXj9xXitzXx+zXnmK3dV8JC7w++/Uxt0/btnvd5qt0kfXs/gJtZ3b7lHpxXwkL1bXbx359zD7CnPr1MV+3dp8pXx/Lga+PvUzbfH1saNsmfn3MPPGR6+tjrq7bp/2uRsK2Uv2/PuZeX4O/PnZXdrMkqSd7vqHttOr456H7/6wDXv3RUeX23mnvDYELbOT29r7k7uV2HBB5P1RoLBC3vb3PRZYNutcn2efuBztj+2O2tf0Ze72huqbQ9dvU8++PqxfZbmh79xUwVxb5WrJq2tfH7D4Tvj7mb/CB/vD1sfC2El8f205Z8tfHbH/MeKx/7NuG6saXmbFc5FfP7DgpR93ofdoogMgxqBT/Hd2XbL/qiR9Iktb3PeX3uR3JXx9bvHix3vve944aEEnS7rvvrk9/+tOSpNtvv32k/KqrrtIzzzyjZcuWjQyIJGnSpEk655xzJEkXXXRRarcAAAAahvEPAAAYDxoaNN3V1TXUSOffmrn11lslSYcddlhN/UWLFqm7u1urVq3Sli1bNHHixEZ2r3HcX0Yjnx5Kbzty9tI9wWP/Ym3aCP3Vx802u4qu7YTw6VwBrO6pKTsT654Kcu9t3F9F3V9AJf/Eln9ax/zlxbzfNuTaJlHa7ihzf2WJffrI/tnHbevbjhb4y/GYpQTmKsdfz+y2kU/1BJ/qcG1HPq0T2U7sE0WSkp7saepfXop4KshdX4PtxF0Pbb+bGeIc2+8SaLnxT+x5EXpSKHahjehFLOKCr+3iEIG69iXGPskZeeoG3x5zs/NPFMS9F7Hh09Eh1QrkNZvuuHqD9qYWdy82D+sE2459Ksg+gGifHooLpB5q2wWL19azgdax9SIDxIPFzXxSOvYhp9infSLrVdw4W4p/AiilLPLJnGBdu8/GPxWU72mmhKeCYsOeQ08KJYRK23M3enyY46IUOc72T1knBFLXY/ucGjZT0d/fr+9973uSRg+A1q5dK0maP39+zTadnZ2aM2eO+vv79cgjjzSqawAAAA3B+AcAALSThj0pdNppp+n+++/X4Ycfrne9610j5evXr5ckTZs2zW43XP7CCy+8bBsLFy605Q888IA61aZPGQEAgLbV7PFPl3bM2WMAAFBmDXlS6MILL9T555+v173udbrssstybTv8tR/7lRcAAIAWxfgHAAC0m7o/KfStb31LJ510kl7/+tfrlltu0YwZM0b9fPgvYcN/MdtWT0/PqHrbs2bNGls+vPoYAABAEVpl/PPQ/X/O020AAFBydZ0UuuCCC3TKKafojW98o2655RbtuuuuNXUWLFige++9V+vWrat5/Lm/v1+PPvqoOjs7NXfu3Hp2rX249LxB/0CXC+Szoa5uOVgbRmsaqbo0v9BfMc2yxbHh0yl/GXUhzIGqNoDavZEu/My+4W5Z3chAavll7m0wXeTSwbEh1cFgw8hl5aOPYeKziNGB1nUWDHaOFRtMZ9vOsW29w6IjQ/bsdSawfXTbscHOLjQwMlwwV9smQNqG28YGRQePYVyYtr92xb1uv3R9jv7gZbXW+Ccz50bkPTZ4nYoLho4PkDbnuLtP2guiAoHWbils047bn+23qRYKKLX7jCy0r9EtGhFXz4VPS4EA6siX40OqTci1GzAEFiexbbu67ji4YZvZ1I2nQkvS2/GPXebebRsZUp24zHzyQh0RQh85v/x85PYpy9QHbkmx27tw5ZRl6u3+AvuMDYGOXireBjPHbTtUNzJUOrrthKDoUHnkeCV2Sfpc43HX99ixV2RZ9GsOSd1+O+r29bHzzjtPp5xyit7ylrfotttuswMiaWgJV0m64YYban62YsUKbdq0SQcccED7rjwGAABKg/EPAABoZ3WZFDr77LN12mmnaeHChbrllls0c+bMYN2lS5dq5syZuuKKK3TvvfeOlPf29urLX/6yJOkzn/lMPboFAADQMIx/AABAu0v++th3v/td/X//3/+njo4OHXTQQbrwwgtr6syePVvLly+XJO244466+OKLtXTpUr3jHe/QsmXLNGPGDF133XVau3atli5dqmOPPTa1WwAAAA3D+AcAAIwHyZNCjz76qCRpYGBAF1xwga3z9re/fWRQJEkf+MAHdMcdd+jcc8/Vj3/8Y/X29mrevHn6xje+oRNPPJGVNwAAQEtj/AMAAMaDSmYTKNvb8Opj+1UObXxjsQM4l4pnq7lkusC2pq4dUJowYx8KbEKPbb3Aa+4wCYE25Ni00xEb4hzZhttfsD8usDm2P5H1AueJDVI2YdG2j7HBzrn6YwpDxzumP06e33ma9QtSnstiZNXo8Gobch5qOyEsOnbb2OC9PP2JDJV2QYJJbQTrFhAq7dqQ4kOlXXB2QUHTWahuxLa+XmOHHXdlN0uSerLnG9pOKxpafexPOuBVHx39AxuiGzleCGxv7w1uYYuU+5yrF2yntpq9l5t+u/fCLtwQuB/aQOJO00cbXGzaMX+ydfUGzZAo2Edbt7Zs0L3uyG1j6w3VHXuwc1LbgVPKnj+x28du6+ToTxGC4w0nNnw6IVQ6T/B1bFi0rRe9bSA0Obad2FBpG9g89m2H6sYGX8e1Xel3Yc+u3cDYIDKUOjbk2i5EElkvWDd2fBk5RkteGOVlgqZXPXm5JGl931N+n9tRt6BpAAAAAAAAtA8mhQAAAAAAAEqISSEAAAAAAIASYlIIAAAAAACghJJXH0MTuYBSl3vsAqxcmKQLKHXh06EsUZcGZ6cdTTsu6MwFRLqw1lAwpmODvE1gtwuZdf1xIWA5gp3tazTpgi6o0+aPD8a37Ts09vBq20piUHRbBC06sUG6KaHQefZZ9/DpHKF4kWVJodJ5gvsiwwCTQqVtf/wxbGqoNMavbc+D2GtxrhBwl65rPtspzbh7mmQv0pXI/ti23a08st5QuWnbfu7su1FbNBBXr2r2NxjsZNw5UDXbD9r31mzsykwA9FBdN2Z0oeRx7bjjZQOpQ6dU5BAvdlziPnJ221B/ogsTJIZK5/qMRGxrf78I3MpjQ6ljA6DtmMh8hl2wc2h7GwJtw6fj2onfNkcYdp1DpX2Qsu1OMaHSkePfYN3YMsO+F3nusbHbjyob+3iPJ4UAAAAAAABKiEkhAAAAAACAEmJSCAAAAAAAoISYFAIAAAAAACghgqZTxQYNu4BSmxTs2ggldCXM6dU5fFqSKq6fg6ZuQvi0CyHMlbvnUv5suHJc+LR7z7LIMOuhynHnT8XtMzJU2oVUh0SHV9uN4+rl6k90zeaJDoGuc/h0rv6kBDbnCdlzIbOxIdD17k8gaDpz5badlD5GBkBLSaHSSUL3lXpvnyu4GA1jP5umWkeOq6479yMXJrDXNBMoHLq+xgdVm31GbhobE53O3cvHHlLtwqelUAB1XIC0C5/O3KIYOW5fNhg6MhjcjbNcqLQ7H4PDsZTtI0Olo8OnW1BsqHR0PXdixNbLUTc2DDk2kDrUn9jtXQh0bIB09P4CYdjRodI2ADqynm0jNGY0ZbHjPnv+uNB+058cY9jkcXE9t20wnhQCAAAAAAAoISaFAAAAAAAASohJIQAAAAAAgBJiUggAAAAAAKCECJpuMZkL7XIhwyFmexeeV8kR9pvStqr1DZ9222amXjBEzIZKm8ajEwJdoFqOoGkXDJ0QKh0dUh2Sp+/biA2QtrXaZXo6IZs3KZA6TwhdSihebFB0npC+IgKkbThpKNi58aHStl4D2NeY2La7B6ENbXtuxN7zkwMvI++TqU27e1XVBYqae6w7x929M/LjLkkVm5iaIi5UOr6eD6B215DB2Dhte82u3dYclqGqJljcdt2WRQanxwZSB7d3FU29hFDp4LvdrADqHKdyUvi0Cy5ODpqODUiO7I8NdvbdiW7bBlLXN1TahT0H+5MQFh0dKh0YV1QGzO9vrm5sWLS7LuQZUyeMTXONlWPazdF2vRYiaZdfxQAAAAAAAFBHTAoBAAAAAACUEJNCAAAAAAAAJcSkEAAAAAAAQAkxKQQAAAAAAFBCrD7WTG4Zi0qOebqE7d2KExWXXu5W5gqknGemrk34L2JFstDqEnaXka/bcQn/doWz+NXH3Gop0auUOQkriuWpm2uVs225PrailJV5Yld1ytNGwkpl0SslNGLlBqfeK40FV3No/Epjvj+B1SEi6wZXU4sRWjKpqO3RfNHnT+K12K5C6ppxq2yaeoGlq9yKMpm917mVz+JWSLNDLNsbKXM/iV0YzK6G5uqZ8UL0imShxs1qYaZe5lZxs5d7t22gN26fbjHYhLLYVcqGtjfvr7tdpKw0lufj1Qarj0WvNJa0IlmelbQi95lUltYfu4JY9Kpgpl7k/sL7TCiLXGnMrTIW3D52BTE3pnLN5BnDpqz+mzp+bgE8KQQAAAAAAFBCTAoBAAAAAACUEJNCAAAAAAAAJcSkEAAAAAAAQAkRNN0GslComQv2tUGoLsQ5NqQ4RwizC0dNCZ82gWo2SNsFUbqEP0mZ3d6FPccGSCcEUgf3GZdOaN9Ht78cyYbR4dWxIaG5UhXHkZRgOiMUbBi9z6Sw58SgvCICpGPDo/NsH7ltdKh0sD8JIc4JryV0X0G5ha41ocUbancQec13YaKuWmgRAhsgbbZ344gOs7vIeqGPcSjYNU5sIrWrFRs+naedlHo52HuVG9dGdscN29ylOLQQibu+R4dKm+Pg3p7IQOpmsgHQIdGh0u5Ym3o2aDrQdmTdlADp6DDr1H3aYOeE/YV+b4wMi3bHKyUUOngMXV33+5IdZ9UW+fMsz0Ikka8xZeGYPGPqsYwvE4Z2PCkEAAAAAABQQkwKAQAAAAAAlBCTQgAAAAAAACXEpBAAAAAAAEAJETTdCLEhxc3kAvXMFGHFBgoHUtZc6HJK+LRtIzZIO7SDuO0zl9TViEDq2KDF2PMnMqQ6pJKSeJhwjkcHXDdZrsDnbeUJZ07ZNk+oXsy2edqud4C0ExsqHQwSdNeAyFDXlFDpHIHSSe9PM6Wc46ifTLXni7sFNWJcEhkIGv0nyVAfY0P6x76pDzINVLXhxW544AKtrbGHTweTi2PHGx2xAdBx4cHB/rgxp71fuKZr92lvDa6NwKXYj4FNPTvMigupdvJ8DF2gdSw7Xs3DBkjXt15s+HRon7aurTf2UOlgiHNKoHWdQ6VtWHNwn6ZuZNhzdNuh8Y89XnH9seezaycx2Dk2YHs8jH94UggAAAAAAKCEmBQCAAAAAAAoISaFAAAAAAAASohJIQAAAAAAgBIiaLrVuKS8ip+7y1zAlwvszbHPmk1d6FauVLy4IDAXPu3YELnY8GnJT4NmLuHNBWybQGq7v8hAtFA7jnt/3LYu4C3P8UoJfE4JQAxl8DYroL0RgXEp+8wTMhzbTkoYcqANG5Ds2OC+yMDmlP0F6sb3O6GPAdFt243jjpe7V6TuE+NAjnPPXaPt/S9+j3G1QteaQbegQ+znOG5bt/BC8LNk7lUuoNSGGdc7fDp4XGLDq+PquaBfGwAdvF+YurFdtGPThDYUOMcj1+6IXh8kV6i027y+YxMbAB0SWzclkNr9uhJqNyVAOrbtyP0F60YGSNtQ+8gQ51xh2LEhzpGB1NGh0sH3LG5MZfsduyBHaih07PaN6E8Dxpzbw5NCAAAAAAAAJcSkEAAAAAAAQAkxKQQAAAAAAFBCTAoBAAAAAACUEEHT+BsXiGWCh0OhgTYwzAUkxwbcmm1t8HVs+LQkuUBHF7odG0htkwBNv0MJfeb9tUHeA5Fh2LaNHHO/oQTGGEWFQqeEYTt5QnhTJAUK59g2MSy6tlpkeF5wBwUFSMdsq4JCpV2Yfq5jWNA5CTSLHW/Eb27ziF2AdIfZ1nwW7bYmHbUSup8OmM98R23dQsKnc91rEkKl7b3YVQzcs10/3Xt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| |
| "text/plain": [ | |
| "<Figure size 1152x576 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "u0_val = np.sin(np.pi * np.linspace(0, 1, 100))\n", | |
| "\n", | |
| "fig, ax = plt.subplots(1, 2, figsize=(8, 4), dpi=144, \n", | |
| " layout='constrained', \n", | |
| " sharex=True)\n", | |
| "ax[0].imshow(fn_analytic(0.9, u0_val))\n", | |
| "ax[0].set(title='Analytical')\n", | |
| "ax[1].imshow(f_out(np.array(0.9), u0_val))\n", | |
| "ax[1].set(title='PINN')\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "00175b1d", | |
| "metadata": {}, | |
| "source": [ | |
| "# Use PINN in PyMC" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "id": "7a0c32fb", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Since we used JAX mode to train, the shared variables end up as JAX arrays. We cast them back to numpy to work\n", | |
| "# with any backend.\n", | |
| "for w in shared_weights:\n", | |
| " w.set_value(np.array(w.get_value()))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "68d194aa", | |
| "metadata": {}, | |
| "source": [ | |
| "## PyMC Model" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "id": "0ea9e573", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Time values we took measurements at\n", | |
| "t_grid = np.linspace(0, 1, 30)\n", | |
| "\n", | |
| "# Location where we measured\n", | |
| "x_loc = 0.5\n", | |
| "\n", | |
| "\n", | |
| "with pm.Model() as m:\n", | |
| " t_values = pm.Data('t_values', np.linspace(0, 1, 30))\n", | |
| " \n", | |
| " alpha_pm = pm.Beta('alpha', 1, 1)\n", | |
| " u0_pm = pm.Normal('u0', 0, 1)\n", | |
| " sigma = pm.HalfNormal('sigma', 1)\n", | |
| " \n", | |
| " # We want the symbolic network, *not* the compiled function we made above (I only made that to generate data)\n", | |
| " # Pass in the random variables for alpha and u0, and fixed values for observed time and space coordinates\n", | |
| " \n", | |
| " # Since our PINN is already written in pytensor, we can just directly use it without any wrappers/etc.\n", | |
| " mu = vectorize_graph(network(pt.stack([alpha_pm, t, x, u0_pm])),\n", | |
| " {t:t_values, x:x_loc} | shared_replacements)\n", | |
| " \n", | |
| " # Measurement error process\n", | |
| " obs = pm.Normal('obs', mu=mu, sigma=sigma)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "98c083b9", | |
| "metadata": {}, | |
| "source": [ | |
| "## Generating Data\n", | |
| "\n", | |
| "Use pm.do to generate draws from the PINN at the values we want to recover.\n", | |
| "\n", | |
| "We only need one sample -- we're going to use it as observed data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "id": "95f82cf4", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Sampling: [obs]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "true_alpha = 0.99\n", | |
| "true_u0 = 0.85\n", | |
| "true_sigma = 0.15\n", | |
| "\n", | |
| "with pm.do(m, {'alpha':true_alpha, 'u0':true_u0, 'sigma':true_sigma}):\n", | |
| " prior = pm.sample_prior_predictive(var_names=['obs'], draws=1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f59f672b", | |
| "metadata": {}, | |
| "source": [ | |
| "The bar is evidently cooling off, but we bought our thermometer on Temu, so it's noisy. Our job is to figure out what the true temperature is." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "id": "d5e48902", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<Figure size 2016x576 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "data = prior.prior.obs.sel(chain=0, draw=0).values\n", | |
| "\n", | |
| "fig, ax = plt.subplots(figsize=(14, 4), dpi=144)\n", | |
| "ax.scatter(t_grid, data, marker='x', c='k')\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "bcce099d", | |
| "metadata": {}, | |
| "source": [ | |
| "## Inference\n", | |
| "\n", | |
| "Use `pm.observe` to try to recover the parameter values, given the data we generated" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "id": "df300ef1", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Initializing NUTS using jitter+adapt_diag...\n", | |
| "Multiprocess sampling (4 chains in 4 jobs)\n", | |
| "NUTS: [alpha, u0, sigma]\n", | |
| "/Users/jessegrabowski/mambaforge/envs/pymc-dev/lib/python3.13/multiprocessing/popen_fork.py:67: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n", | |
| " self.pid = os.fork()\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "application/vnd.jupyter.widget-view+json": { | |
| "model_id": "c6b792860ef64ecc8a395ecc64c8a07f", | |
| "version_major": 2, | |
| "version_minor": 0 | |
| }, | |
| "text/plain": [ | |
| "Output()" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/Users/jessegrabowski/mambaforge/envs/pymc-dev/lib/python3.13/multiprocessing/popen_fork.py:67: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n", | |
| " self.pid = os.fork()\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" | |
| ], | |
| "text/plain": [] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 24 seconds.\n", | |
| "Sampling: [obs]\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "application/vnd.jupyter.widget-view+json": { | |
| "model_id": "5a3bcad8ab824c42a1c689c7c0931c32", | |
| "version_major": 2, | |
| "version_minor": 0 | |
| }, | |
| "text/plain": [ | |
| "Output()" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" | |
| ], | |
| "text/plain": [] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "with pm.observe(m, {'obs':data}):\n", | |
| " idata = pm.sample(target_accept=0.9)\n", | |
| " idata = pm.sample_posterior_predictive(idata, extend_inferencedata=True)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "d62fbb81", | |
| "metadata": {}, | |
| "source": [ | |
| "## Results\n", | |
| "\n", | |
| "Not perfect, but seems reasonable.\n", | |
| "\n", | |
| "If we observed more data -- either more points on the rod, or more time points, we could get better estimates." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "id": "62ff4965", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([<Axes: title={'center': 'alpha'}>, <Axes: title={'center': 'u0'}>,\n", | |
| " <Axes: title={'center': 'sigma'}>], dtype=object)" | |
| ] | |
| }, | |
| "execution_count": 18, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
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", | |
| "text/plain": [ | |
| "<Figure size 2208x552 with 3 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "pm.plot_posterior(idata, var_names=['alpha', 'u0', 'sigma'],\n", | |
| " ref_val=[true_alpha, true_u0, true_sigma])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 19, | |
| "id": "4eb5d3df", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.collections.FillBetweenPolyCollection at 0x168bfb9d0>" | |
| ] | |
| }, | |
| "execution_count": 19, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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zu9PasSGtHd0t6kqv7t85nufpyiuvnLL93nvvlWXR3QZAc2jUNaR6oNFs+wEAWCpM7wIAQPOhAn/prIkKfABLK2aZumBTq7a0J/XEyYyGJwo6NpbTSKaoszqSSsd5OwCWCh9SYDWJ26Z2bmzRzo0tNdvHc065Sr9Utf/0SK5hG34/kJ4eyenpkZyGHj1V3t6asMNQf0OlDf/2rvSqqNYPAl/9/bc13NfffxvBF4Cm0ahrSOn2wIGD6u+/jfAeALDsmN4FAABg7kjsgHWmNWHreds6dHKyoI5UTCcm8np6JKeWuK3N7QnFLD64AxYTH1JgrWhPxfS8bR163rbaNvzD44Vytf4vTmf0i9NZHR8vNDzHZMHVfz07rv96dry8zTSkrR1htf6OKNg/tzut7pZ401TrN6pWrTZdi2oAWCnThfj172OE9wCA5cD0LgAAAGeGAB9Ypza2JtSVjuuZ0Zw6UjmdmMjrsROT2tCaUHdLXGaThCbAasaHFFjrTMPQWR1JndWR1G/s7C5vzxU9PTUShvpPnqpU7Occb8o5/ED65WhOvxzN6f7Hplbrl782pHXOClTrT9dqur6KlRAfQLNpFOJXI7wHACyXnp492rdv77R/O0/3N3dPz54VuV4AAICVRoAPrGOWaeic7rQ2tSX05Kmsjo3ndHysoMeyk9rcnmS+E2CB+JACa9Vs00Kk4pZ2bW7RiZ//SH/00nAwShAEOjERVus/WarYP5XV8fG8ggbnaFStbxjS1vZkVKnfonOjYH/DElXrzzZP9HQtqgnEADQLwzB14MDBhgH+gQMHea8CACwLpncBAAA4MwT4AJSMWbr4rDad1Z7UE6mMTkwU9Ox4XiOZos7qSCphWyt9icCqxIcUWIvmOy2EYRja3J7U5vakXnRepVo/73h6eiSs1K+04s8qW5xarR8E0jNjeT0zltf3Hztd3t4St3ROVaX+ud0t2t6VUjK2sN9fQ0P3z/gzOt3PeG/vS+miAaApBIGv/v7bGu7r77+NvzsAAMuG6V0AAADmzgiCoFHRExbR7t27JUlHjx5d4SsBZhcEgY6N5/XU6axOTBR0YrKgjmRcm9oSskza6gPzMdv82RIfUmB1GBwc1E033VReb/R92+j7/ZZbbjmjQDsIAp2cLEYt+DPlUP/YWONq/UYMSWd1JGta8J/bndbG1sQZVevPd8ACAKw0/v4AADSjmX4/8XsJAIDl9/jJjLa0J/Tind10ZV5kC8mHCfCXAQE+ViPH8/XU6ayeGc3p+ERBk3lXm9oS6kzFlqRNMbDW8SEF1oLZWsrPtn+hCq6np0dyVdX6Gf3iVFaZBtX600nFrJpAf0d3Wud0p2es1p9tygAp/LcZGrqfynsATWG692M6AAEAmoHnebryyiunbL/33ntlWXSBBABgORHgLx0C/CZHgI/VLFNw9fjJjIYnCjo2llMQhBWN6TgzcABnig8psBY0WygUBIFOZ4o1LfifPJ3Rs2N5zfWvXEPSlvZkOdgvVe1vakvIZNAagFVmpQdbAQAwEwa3AwDQXAjwl85C8mESOAAzaknYet62Dp2cLKgjFdOJibyeHsmpJW5rc3tCMYv/VAFzwRy0WCuabe5KwzC0oTWhDa0JvfDcrvL2ouvrqZFKqP+LU2GwnylMrdYPJB0bz+vYeF4PPnG6vD0Vs3ROd0o7ulu0ozutczekdU5XWqk4A24ANK+hoftnDOenex/v7X0pXUQAAEtqtuldStv5/zEAAFjvCPABzMnG1oS60nE9M5pTRyqnExN5PXZiUt0tCW1ojVOhCMyADymw1jQKf6o1Q+VM3DZ1waZWXbCptbwtCAKNZB09eSoTVeqHwf6zYzn5Dar1c46nh49P6uHjkzXbN7cltKM7re1dKW3rSmtbZ0pbO5IztuEHgOXS29urvr4+DQwMTPt+XP8+3tfXR3gPAFhSc+3kxf+PAQAAaKG/LGihj7Um73j6xekw8Dg+VlDB9bS5PUl7FaCBZms3DiymtTItRNH19cvRnH5xOhNV6mf15KmsJgvuGZ1nY2tc2zpT2taZ0tldqfJyG78fAayAwcFB9fTsmfHviiDwNTR0P+E9AGBJMb0LAADNixb6S4cW+gCWVTJm6aItbdrSltQTqYxOTBR0bDyvkUxRW9qpQARKZvsQolH7WolKA6wOa2laiLhtaufGFu3c2FLeVqrWr7TgD6v2nxnNy5tm/OvJyaJOThb1f58eq9nenrR1dhTmb6sK9rtb4jLoYANgicwllDcMk/AeALDkmN4FAADgzBDgA5i3jnRMz0916Ph4Qe0pWycmCnrydEYdybg2tSVkmYQSWN/4kAJr1XqYFsIwDHW3xNXdEtevndNZ3u54YbX+U6ez+uVoTr8cyemZ0ZyOjecbtuGXpPG8q/FjE/rZsYma7cmYqbM7plbsb2lP8jsUAAAAawbTuwAAAJwZWugvA1roYz1wPF9Pnc7qmdGchicKmsi72tSWUGcqRnUh1rXDhw/P+CGFVBuG9vX1af/+/ct/ocAcMS1EY67n69h4vibU/+VoTs+M5lX0/DM6l2UaOqs9WVOtf3ZnSmd3JpWw6XIDAACA1YnpXQAAaD600F86C8mHCfCXAQE+1pNMwdXjJ8O2+s+O5eQH0taOpNJxGn5g/eJDCqwVzF155vwg0MmJQhjsj1aC/V+O5pQpeGd0LkPSxtaEtnWlKi35o6/WJL9nAQAAAAAAcGYI8JfOQvJhPukDsKhaEraet61DJycLak/FdGIir6dHckrHLW1pTypmrc8AB+sbc9BirWBaiDNnGoY2tye1uT2pX9/RVd4eBIHGck5VoJ8vB/ynM8WG5woknZgs6MRkQf/51GjNvo5UrFypv60zVa7e70rTCQcAAAAAAABYTQjwASyJja0JdaXjemY0p45UTicm8nrsxKS6WxLa0BqXSZgAAKsOc1cuHsMw1JmOqzMd13PP7qjZly26eqYq0C+15T8+kdd0vbPGco7Gco7+69nxmu2pmKWzO5OVVvxRsL+5LSnL5HcxAAAAAGDu6DIJrH5z+Tn2fV/f/OY3dfXVVy/jlaEaLfSXAS30sd7lHU+/OJ3Vs2M5DY8XlCt62tKRpB0LAKxS/Id9ZTier2Nj+XIL/l+O5vTMSE7PjOXkeGf2J71tGtrakQwr9rsqrfi3dqQUt+mWAwAAAODM8X/Fte3w4cMzDuiXaqfe6+vr0/79+5f/QgFMq9HPcX0Lfd/3dcMNN+hLX/qSbr75Zn3wgx9c6ctetRaSDxPgLwMCfCA0lnX0xKmMTkwUdGw8L9s0tKU9qWTMWulLAwBg1fL9QCcmC+VK/erK/WzRO6NzGZI2tSXKbfjLLfk7U2pJ0LwLAAAAQGOEu2vb4OCgbrrppvJ6o9e5+vUtueWWWxisATSJ6X6OnziVKwf4rXGrHN6X/NM//ROV+PO0kHyYT+EALJuOdEzPT3Xo+HhB7SlbJyaKevJ0Rh3JuDa1JWjlCwDAPJjRgLgt7Um9cEdXeXsQBBrNOfrlSFUr/uhrNOs0PFcgaXiioOGJgv7jqdGafe1JWxtbE9FXXBvbEuX1Ta0JtSQsGUyRAwAAAKw7g4ODGhgYkKRyeDtbuDswMKBdu3YR7q4SPT17tG/f3vLrV/86Nwrv9+3bq56ePStyvQCmmu7n+FXX/6kkRZX3b6kJ76+//nq98pWvXP6LBQE+gOVlGIbO6khqQ2tcT53OqmPM1vB4QY+emNTG1oS60jE+/AcAYBEYhqGudFxd6biet62jZl+m4NaE+qXl4fGCpmvPNZ53NZ539djJTMP9yZipDS0JbWqLAv7WRE3g35WOy2SwHgAAALDmEO6ufYZh6tChQ5I05XU+cOCg+vtvm/L6TteJAcDKmO7nOGu16uCf3qC333ijvlwX3t9+++0yTX6OVwIt9JcBLfSB6WUKrp44ldHweEHHxnPyfGlrR1LpOOOLAABYbkXX17Nj9RX7eT07mpPrL+y/DZZhaENrXBuicH9TKdyPAv8NLQnFbf5TCAAAAKxG04X0hLtrS6PXuR6vL9Dc6n+O7a6t8iZPq/D0fykoZiUR3i8WWugDWLVaErZ+5ewObWkvqP1UTCcm8np6JKd03NKW9qRiFr8gAABYLnHb1LkbWnTuhpaa7b4faCRb1MnJok5OFnRisqCTEwWdnCyUtxVcf8Zze0FQbs8vTTQ8piMVK1fvb2pLaENLQhvb4uWwvyXBf18AAACAZjRdZWd90Eu4u7o1ep2r8foCzW+2n2PC++ZABf4yoAIfmBvPD/TMaE5Pj+R0YiKv05miulsS2tAal0lbfQAAmlYQBJosuGGYP1HQyUwp4C/qxGRBpyYLGs+7C36cVMyqtOdvS0SV/HFtiAL+znSMvxkArBuDg4Pq6dkz4wfkQeBraOh+5hdepXiNAaxGM1VoE+6uHZ7n6corr5yy/d5775VlWStwRQDOVOnnuL4C33Ec2TYFFIuBCnwAa4JlGjqnO61NbQn94nRWz46Fc/E+Ojyp9lRMMcuUbRmKmaZiliHLNGTwIT0AACvOMAy1JWNqS8a0c2NLw2MKrlcJ+Cdrq/dPThZ0OlPUbF36c46np0Zyemok13C/bRrlFv3hV2V5U1tC3S1xuvsAWBMOHz6sgYGBGYOQ6gClr69P+/fvX/4LxbzxGgNYrQzD1IEDBxsG+AcOHCS8XwOCwFd//20N9/X338YgDWAVmOnn+M1vfjMV+E2AAB9A00nGLF20pU1b2pN64mRGJycLyhRdFVxPkwVfrhfI8Xx5gRQzDdlWGOjHLFO2aVSC/midkB8AgJWXsC1t60xpW2eq4X7PD3Q6U9SpUov+UrhfrugvqujN3Kbf9QMdHy/o+Hih4X5DUkc6Vm7Jv7E1Hlbyt5Qq+uNKx/kvEoDmNjg4qIGBAUmVlpf1H5TXVz8ODAxo165dVGmvErzGAFYzwt21baYOC9L0v7cANI/Zfo6/9KUvSRIh/grj0ykATasjFdPzt3fodKaonOOp6Poqen54G305fiXQL93mHE+O58vxAnl+IMs0Ggb7Mcssb6PdLoCFoL0psHCWaWhTW1gp/5wG+4Mg0ETejcL9gk5F7fkrFf1FTRZmbtMfSBrNOhrNOnpkeLLhMS1xq9yif1NUub+ptN6WUGuC/0IBWFk9PXu0b9/emvmFpcoH5Y0+kNu3b696evasyPXizPEaA1itCHfXtul+/xw4cFD9/bdN+3sLQPNo9HPc29urg396g778yQ/qy//ri5II8ZsBnz4BaGqGYWhDa6LhPt8PVPR8FUqBfl24X/TC0L863Hf98LbghPd1/UCu58s0KuF+dVV/ubrfNGWahPwApqK9KbA8DMNQeyqm9lRMF2xqbXhM3vHKLflPTBSjoD8M909MFjSSLSqYpU1/pugpczqrJ09nG+5Px61ysF8d8m+OAn4q+AEsNcMwdejQIUma8kF5/QfoEvMNr0a8xgBWI8LdtW2617f0Ok73e4vXGWge0/0cv+qNb5RpWfrMZz8rO3DL4T0h/soygmC2j7CwULt375YkHT16dIWvBFh/giBQIQrx60P+QtW641bCfCe6LXq165LK1ft2XdBfquS3+UUGrCuDg4O66aabyuuNPjxt9MfxLbfcQiU+sAJc39fpyaJOZopVlftV7fonC3K8hf33qCVuTQn2q9cJ+AEsltmqHCWC3dWO1xjAajFbuDvbfjQ/Pv8AVr/pfo6fOJXTlvaEXryzW61xSzfccEM5vJekf/qnf9LVV1+9Epe86i0kH+bTIwBrmmEYSsYsJWPWtMcEQSDHCxpW8Beq2/VXVfCXKvrzrqfJQtiu3/V8+YEqlftmVcv+qIo/ZhmyTEMGLfuBNYH2psDqYpumNrcntbk9KW2duj8IAo3lnHKgf2KioBOl2yjwL7j+jI+RKXrKnMrqyVONK/hbEpUK/k1tyarlMORPxaf/mwUAqjWqdqtGMLL68RoDWC2Ghu6fMZyfrkK7t/elhLurRG9vr/r6+mbsQFj/Ovf19fH6Ak1kLj/Hpmnq9ttvlxRW4N98882E9yuECvxlQAU+sDY4Xm2YX6hv2x8tu14Y6Dt+GPSX1sNqfl+ur6nV+9Vt+6Ogn5AfWB3m2iawtJ0PWYHVKwgCjefdcqBfCvdPThY0PJHXiYmFV/C3JuyaQL/mti0x46BEAOuT53m68sorp2y/9957ZVm8Z6wFvMYAVgOml1sfBgcH1dOzZ8bPNYLA19DQ/YT3QJOq/zl+/GSmXIHfnoxJknzf1ze/+U3C+wVaSD5MgL8MCPCB9cPzg0qLfs+bEu6XBwD4lSr+8m1U3e94gfwgUHsyps50jFa7wCpAe1MAUnUFf6Em5B+eKOhktLzQgL8taU+p2i8tb2wl4AfWm5n+BuFvj7WB1xjAakK4CwCrT6MAH4uDFvoA0CQs01AqbkXtbxv/svP9sF1/oaqavzrkL7i+sgVXozlHz4zmZBiGOlMxdaRjsk0+mAGaEe1NAUjh1D2d6bg603FduLltyn4/CDSec6YG+9H6yTkE/BN5VxN5V4+dzDTc3560y2H+5rbqoD+pjW1xJWwCfmCtmG0AYf3UPlh9eI0BrDZzCeUNwyS8BwBgFgT4ALDMTNNQ0rRmrJDLFb1yK97RnKPRbFEnhgtqS5Sq8i1a7ANNxjBMHThwsOEHrAcOHORDVQAyqwL+XVsaB/xjpYC/rk1/qVW/688c8I/nXY3nXT16YpqAPxULg/3WStV+KeTf0BKngh9YJeY6hQ8B7+rFawwAAACsXwT4ANCEUnFL525o0TldaY1kixqeKOjUZEFjOVfHx/PygyAMAFIx2RYf0gDNIAh89fff1nBff/9tfKgKYFamYagrHVdXOq6Lpgn4R7POlGA/XM7r5GRR3mwBf87ReM7Rz4cnG+5Pxkx1puLqTMfUkYpFAw5i6kzFom1xdaVjak/GZJoMJgRWwnTBbulvjfquQAS8qw+vMQAAALC+EeADQBMzTUMbWhPa0JpQ3vF0YiJstzsWVeU/emJS6bitznRMrQmbqnxghdDeFMByMA1D3S1xdbfEdbEaBPx+oJFscUrV/nC0fGqyKC+YOeDPO76OOXkdG8/PeJxhSO3JSrDfmY6rIxVTVxTyV0L/uJIxk79RgEU0NHT/tMGu1Hhqn7vuulu9vS+lZfEqwWsMAAAArG8E+ACwSiRjls7pTmt7V0pjOac8b+5YztHJyYKeHcuXPyiP2wSEwHKhvSmAZlE98O85Z03dXw74o6r94YnaoH8kW5TjzRzwlwSBNJZzNJZz9OTpmY9N2GYU7sfVEQX79eulAQAWVf3ArHp7e9XX16eBgYEpwW5JfcDb19dHsLuK8BoDAAAA65sRBLOUYGDBdu/eLUk6evToCl8JgLWm6PrlyrrRbFEjmaLGco6SMUud6bjakrZMKt6AJTNbe9PZ9gNAMwmCQNmip9Gso9FcMbyNlseyjkZyjsayRY3mHE3k3UV/fENSW9JWRzqurlSsJtwvVfR3pMMW/qmYRVU/1r3BwUH19OyZ8W+KIPA1NHQ/we4qxWsMAACApfb4yYy2tCf04p3dak/GVvpy1pSF5MME+MuAAB/AchjPOxoeD6vySx+65x0/mr82pmTMWulLBNacwcFB3XTTTeX1RuF8oxD/lltu4UNWAKua6/sayzoazTlRuF8sr49mw79DxnLOGVX1n4mYZaiz1Kq/um1/OlbZHlX62xYDpgAAAAAAaIQAf+ksJB+mhT4ArBHtyZjakzGdtyGtU5mijo/nNZINP0z/xemsYpYZfsCdjMmkPS2wKGhvCmC9sk2z3K5/JkEQKOeUqvqnhvvVof9E3tVco37HC3RiMpwKYDatCTsK9+NRRX8l5O9qias7HVd3C1MQAQAAAACA5kAF/jKgAh/ASpksuBoez+vkZCGsjss6yhRdtSfDD6/TccZxAYuB9qYAsHCu72s854Yhf1TZXw79S5X+0QCAoucv+uO3Juwo0I+puyUeLlcF/F0tcbUlbFr3AwAAAADWDCrwlw4V+ACAhloTtlo3tercDS06lSloeLygkUz4IfgzozkZhhHNJxuTbVJ1BszXXEJ5wzAJ7wFgBrZphoF5S3zG44IgUN7xy8F+WNFf1EhU2V+q8h/NORrPOXOu6p8suJosuHrq9PTHxCxDXVWBfincL311pePqStO2HwAAAAAAzB8BPgCsA5ZpaHNbUpvbksoVPQ1P5HViolCuajsxXIjay8bVEreoLAMArCt00VhdDMNQKm4pFU9pa2dqxmM9P9B4vi7kj8L9kWxRI5miTmfCwN+bQ3M6xws0PFHQ8MTMrfs7UrFyoN/dElNXOq4NrfFy+N/dElcqxt9cAAAAAABgKgJ8AFhnUnFL525o0TldaY1kixqeKOjUZEFjubDdvh8E6ojmhY1RPQYAWOMOHz6sgYEB7du3V4cOHWoY4geBr1tvvVV33XW3+vr6tH///uW/UMyLZRpRVXxcUsu0x/lR0H8qE4X6VeH+6fK6o5zjzelxx3JhN4DHlZn2mIRtakNVJX9Xy9Rq/s5UTKZJyA8AAAAAwHpCgA8A65RpGtrQmtCG1oTyjqcTEwWdmCyELWezRT12YlKpuK3OdIz5XgEAa9Lg4KAGBgYkSXfddbckTQnxq8N7SRoYGNCuXbuoxF9jTNNQZzquznRc2jT9cbmiVw73pwv7x+bYtr/g+npmLK9nxvLTX5chdZaq9kshfzqm7taEutOxcuifsK0zf9IAAAAAAKApEeADAJSMWTqnO63tXSmN5RwNTxR0cqKgsbyjU5MFHRvLqzMVU2c6rrhNVT4AYG3o6dmjffv2lsP5+hC/PryXpH379qqnZ8+KXC9WXipuaVs8pW0ztO53fV9jWadcuV8K9keqKvlPZ4oqev6sj+cHKt9/Ji1xK6zaj4L+8nJLJfxvSzIgEwAAAACA1YAAHwBQZhiV6rPzNrTo5GQ4x+tYtqiRbFGPn5xUMmapM/oQ2ORDYADAKmYYpg4dOiRJU0L8AwcOqr//tinh/XRt9oES2zTLXY6mEwSBMgWvHPCPTBP2T+TdOT1mpugpU8zpqZHcDNdlqDMdU0cq/GpPxtRRtV7enoqpNcHfeQAAAAAArBQCfABAQ3Hb1NmdKZ3dmdJ43tHweFiVP5orajRb1LNjOXWm4upMx5SM0bYVALA6TRfiVwf3EuE9FpdhGGpN2mpN2trRnZ72uKLrayRbG/BPCfuzjjx/9qb9rh/o5GRRJydnruaXJMsw1JayK8H+DGF/ezImyyTsBwAAAABgsRDgAwBm1Z4MP5w9b0NapzJFDY8XdDpb0FjW0S9OZxWzzLCiKxmTyQe4AIBVplGIX43wHislbpva0p7UlvbktMf4QaCJvFsO9MNQvxL2n4rWs0Vvzo/rBYFGs45Gs86sxxqSWpN2TahfH/RXf8Usfo4AAAAAAJgJAT4AYM5sq/Ih8mTB1YmJgk5M5DWWdTSSdXR8PK/2ZEyd6ZjScX7FAABWD8MwdeDAwYYB/oEDBwnv0bRMwyiH4zs3tkx7XN7xNJZzGn6N162fSdgfSJrIu5rIu3p6hhb+Jem4Neewny5PAAAAAID1iHQFADAvrQlbrYmw7evpTFHDE3mdnixqNOfomdGcDMNQZypst2qbhB4AgOYWBL76+29ruK+//zYq8LHqJWOWkjFrxmr+kqLrazw/t7B/Mu9q9gb+Fdmip2zR07Nj+VmPTdjmrGF/aXtL3JJh0AkKAAAAALD6EeADABbEMg1taktoU1tCuaIXVuVP5jWSdTSaLerEcEGtCVud6TgfrAIAmlIQ+Lr11lsbVt9Llbb6hPhYL+K2qY2tCW1sTcx6rOcHGs9PDfbHco7Gso7G8rXhv38GaX/B9TU8UdDwRGHWY23TmBLytydtpeO20nFLqbhVXi59peK20jGLKaAAAAAAAE2FAB8AsGhScUs7NqS1vSulkWxRwxMFnZosaCznang8L88P1JmOqzPN/KcAgObQKLzft2+vDhw4qP7+28rbCfGBxizTUFc6rq50fNZj/SDQZMHVWNaZWuHfYJvjzT3td/1ApzNFnc4Uz/g5JGNmXbhvh4F/rLLOIAAAAAAAwHIhwAcALDrTNLShNaENrQnlnVJVfkGjUVX+YycnlYrZ6kzH1JawqcoHAKyI6cL7Ukh/6NAhSSLEBxaJaRhqT8bUnozNemwQBMo53pQq/nJlf6428M87/ryvK+/4yjtFnc7M+xTlQQCpmFUzEKB+mUEAAAAAAIDZEOADAJZUMmbpnO6wKn8s52h4oqCTEwWN5R2dmizo2FheHamYUnFLtmnIMg3ZpimLDzABAEtsaOj+acN7SdOG+L29L1Vvb+/yXzCwjhiGEQXdtrYqNevxBdcrB/ulwH8i7ypX9JQtusoWveirspwreso53qJcb2kQwELMNAigPvgvrbcwCAAAAAAA1hwCfADAsjAMI2qfH9d5G1p0cjKcz3QsW9RoNqykcn1fnh+EX4GqAv0w1Letynp10G+bBh9WAgDOWG9vr/r6+jQwMDAlvC+pD/H7+voI74EmlLAtbW63tLk9eUb38/2w0r8U7udKQb9TCfvrBwFMWW+iQQBxy1TcNpWIvsJlq7ytcmvVrUe3lqVErPr+U4+zTTqQAAAAAMBSIsAHACy7uG3q7M6Uzu5MaTzv6NRkUUXXl+OVvgK5ni/X9+X6kuf7cv1AnhfI9X0V3HCb5wVyg/BYQ1Gob5l1IX9lu121Ttt+AIAk7d+/X7t27VJPz55p2+KXQnwq74G1xzQNtSRstSRsSYl5ncMPAuUdT5nCyg8CKHq+ip6vycKinK4hyzAaDAhoNFDAqhtIMN3AgakDDGKWKZO/1wEAAACsUwT4AIAVNd08qL4fqOiFwb3j+nJ8X64XlAN+xwvXi54fhf1huB+G/GEVv+OHAwLyThDtD8qDAUyjtoLfNo2owt+sCv3DW8sg8AeAtWwuobxhmIT3ABoyq9r9L3QQQH2r/9mmAKhezzuegsV9ag15Qdi1YLEGHUynpptALAr6rdqgPxmzwgEYcas8EKM1um2JW2pN2krGLAYDAAAAAFhVCPABAE3JNA0lTStcmcPnoKUQv+hVB/0NQn+/UuEfhvyBPK9S6V9wPWX98FgvkLzodkpFfyn8t+ra/NPOHwAAAGeodhDA/PhB+DdswfVVdKtvvfDW8VXwqtZrjvOmv1/V9oLryV+OUQJavG4ChiG1xEvBvqWWuF0V9lcF//Fof9UggIRtMpAXAAAAwLJrqgD/6aef1gc+8AHdfffdOnXqlLZu3aprrrlGN998s7q6upb0PENDQ7rlllv0/e9/X/l8XhdeeKHe9KY36cYbb5RlWYv1FAEAS8S2TNmWlIzN/p4dBGE1fn01f3ULf6dU/R9V+DueL8+XvFKlvx/I9QLlHL88GKBU+R9UB/5WbZV/KfyPR5VDAAAAwGIwDSNqW790n2EEQfj3bmGWoL/oNRoQUBkoUJhl4IDjLd4ogSCQJguuJgvuGd/XiqZYaK2q8K+u7q8MBrDC0D9e6QLA3/oAAAAA5qtpAvxHH31UPT09Gh4e1tVXX63nPOc5evDBB/XpT39ad999twYHB7Vhw4YlOc+dd96pa6+9VslkUq95zWvU3d2tb37zm3rXu96lwcFBfe1rX1uqpw0AWAGGYShmGYpZc/tQzY/a8U/bwt/35bhRy363tp2/5wdygzDsd31feTfclnc8JWxLXem42pI2lT0AAABoeoYRdqCyLVMt85stYE78IFBxto4Anq9c0VWm4ClTdDWZd5WJ1icLrjKFcD3v+PO+Ds8PNJ5zNJ5zzvi+McuIwv6qtv6loL+0Pdmo/b8l2yT8Xy8GBwfV07NHhjH9ax4EvoaG7mcqHwAAgHWkaQL8P/3TP9Xw8LA+85nP6MYbbyxvf/e7361PfvKTet/73qfPf/7zi36e8fFx/fEf/7Esy9J3vvMdvehFL5IkfeQjH9HLX/5y3XHHHfrqV7+q1772tYv4bAEAq4lpGkqYlhJz/K3p+Q1a+PtBFO77KrqBJvKORrJFncoUdGw8r650XF3pmOw5DioAAAAA1irTMJSMWXPqrjUb1/OVKXphoB9V4pfWy0F/wdVkwSuH/qV9C+kE4HiBRrOORrNnHv4nbHNq6B9V96fjllJxS6lY5TYdt5SK2UrGTKXi4b+byQDhpnf48GENDAxo3769OnToUMMQPwh83XrrrbrrrrvV19en/fv3L/+FAgAAYNkZQRAs0+xl03vsscd0wQUX6LzzztOjjz4qs2qk8cTEhLZu3aogCDQ8PKyWlpZFPc//+l//S3/0R3+kN77xjRoYGKg535EjR3TFFVfo0ksv1Xe/+915P7/du3dLko4ePTrvcwAA1hbX83VisqDj4wWNZos6nSlqPOeoJWGrKx1Xy1xHCwAAAABYEkXXn7G6P9xeGRyQKbiajNY9f2U/bqsO+KfcTrMv3WA7A4yXxuDgoG666abyeqMQvzq8L7nllluoxAcAAIvq8ZMZbWlP6MU7u9WejK305awpC8mHmyIdOHLkiCTpqquuqgndJamtrU29vb2655579P3vf19XXHHFop6ndJ+9e/dOOd+ll16qdDqtoaEhFQoFJRIz94crvRD1fvrTn+qSSy6Z8b4AgPXFtkxt7Uhpa0dKY1lHxyfyOjGR12jW1bPjeRmSutJxdaZiMk2qZwAAAIDlFrdNxe24utLxM7pfEAQquH5dlb+nyWJdxX/RVaZ+cEDR1WKU2uQcTznHW/B5YpbRIPC3a6r/k7EGgwDqBgIkbJNpw6r09OzRvn17y+F86bYU4jcK7/ft26uenj0rcr0AAABYXk0R4D/00EOSpIsuuqjh/l27dumee+7Rww8/PGOAP5/zzHQf27a1c+dO/eQnP9Fjjz1GCA8AWBId6Zg60jGduyGt4fGChifyGsk6GskUNTyRV0cqpq50fFFaiAIAAABYWkbVFAAbWmcuBqnnB4Hyjlfb1r9qIEDO8ZQthuF83vGUi5ZzRU/Z6Lbg+ov2XBwvkOO5Gs+7CzqPYWja6v903eCAZNwsDwRI2JZiliHLNGWbhmzLkG2a0W3t8moaIGAYpg4dOiRJU0L8AwcOqr//tinh/XRt9gEAALD2NEWAPzY2Jknq6OhouL+0fXR0dNHPs1iPLU3fAmG6ynwAAKolbEvndKe1rTOl09mijo3ldTpT0GjW0S9OZxS3LXWn42pL2qvqwykAAABgoQYHB9XTs2fGADMIfA0N3b+qW4ybhqF03FY6bmtT2/zO4fnhIIBcXcBffZutWXcr+x1fuaJb3rdYMwEEgZQtho+rzOKcs55lGrUh/3TLpfDfirZXLVumoZjVeICAVTdwIGZNPX/9QIOYVX+OykCD6UL86uBeIrwHAABYj5oiwJ9NEPUOW2hYMZ/zLNZjAwAwV6ZpaGNrQhtbE8oWXR0by+vEREGj2aJOZws6Np5XVzqmznRcMeakBAAAwBp3+PBhDQwMzBhkVrcc7+vr0/79+5f/QpuEZRpqSdhqSSzsY78gCFT0/DDcr6rwr67+z84wSKD6tugtXleA6Xh+IM8PVHAlaeHTByyVKQMNtv+2zn3NizU5MSH5ngLfVeA6CjxHWzZtUPqS5+iL//ZEOKWDZShum4pZZrReuY1Vrdfvj0X3s03+/wgAALAaNEWAX6pyL1XD1xsfH685bjHPs1iPDQDAUkjHbZ2/qVU7utM6OVnUsfG8RrNFjWSKeuzEpNJxW90t8QV/OAcAAAA0o8HBQQ0MDEiaOk94Sf184QMDA9q1a9eqrsRvBoZhKGGHbew70ws7l+v7yhd95Ry3rvq/6ra0XLW94PpyfV+uF8j1g2mXvcVqFbAMGg40sNKKNfhHHpM0+OipRXts01BdsN8g9K/bXho0UD9IgEEDAAAAS6cpPu2/+OKLJUkPP/xww/2PPPKIpOnntl/IeS6++GL98Ic/1MMPPzyl1b3runr88cdl27bOP//8OTwTAACWhm2ZOqsjqbM6khrLOTo+ntfJiYJGc46OjecVBFJ3S1wdqZgsk64xAAAAWBt6evZo3769U+YJL4X49eG9FLYc7+nZsyLXi8Zs01Rr0lRrcmk+igyCMBR3vCjY94Mo3K8O+SvLjld3TLTs1d3XKQ0W8Hx5fmXZrV/2ph9c0EwDDfxAyju+8s7Sd0QomW3QQCIaNBDeWkrYphIxUwmrsl7an4hVrVul7ZYSsXDqAjqoAgCAtaIpAvzLL79cknTPPffI932ZVSMzJyYmNDg4qFQqpZe85CWLfp6Xv/zl+spXvqK7775bf/AHf1Bzvu9973vKZrO69NJLlUgkFvw8AQBYDB2pmDpSMZ27Ia3h8YKGJ/IayToazRQ1PJFXRzKmrpa4kjFrpS8VAICmsF7mzgbWounmCZekAwcOqr//tinhPfOFrz+GEbWktySpef8f5EcDDSoDBDz9//7y8/rO9/5dhmlJpi3DismwwltZtl7wwt367av2quiFAw+Knq+iG345Xuk2qGyv31+1PViB8QPLNWjAMFQZBBCF+8lYJeQvhf6J2NSBAXHbVLJ0jF17n2TVesxikAAAAFgeTRHgX3DBBbrqqqt0zz336HOf+5xuvPHG8r6bb75ZmUxGb3nLW9TS0iJJchxHjz76qGKxmC644IJ5n0eSrrvuOr3nPe/RV7/6Vd1444160YteJEnK5/O66aabJElvfetbl/T5AwAwHwnb0jndaW3vSul0Jmyvf3qyqJFsUb84nVXMMtXdEldb0pbJhwwAgHWKubOB1W+6EL86uJcI79H8TMOQaRmKWVIQGLr11k/o23UDUOoHpjz41I+1oXh8wd/bpS4FRa86/K8N/h3XnzoQwKsMFKgeNBBuD6YMGqg5fhkHDQTLMFDAkBqG/NMPAqjqKmBXpigwZUhGOOjAkCEjOrmhqm3Rf+ENw6jaHi4YUvk+pf/rl45RdF8juq+q76uq46PHkSGZ5cevetzSY1fdt3Q+s+7aVPV4leuonM80DFmmIdMQAyAAAJgjIwhWYuzlVI8++qh6eno0PDysq6++WpdccokeeOAB3Xfffbrooos0NDSkDRs2SJKeeOIJ7dy5U+eee66eeOKJeZ+n5J/+6Z903XXXKZlM6rWvfa26u7v1jW98Qw899JCuu+46/f3f//2C/rgoteY/evTovM8BAMBcZIuujo8XNDye12i2qJGso4LrqzMVVuXHLD7MBACsH4ODg+WB2VLjcK9R++1bbrmFSvxVhi4L60Ojn9cSwnusJtNN/TDb1BCr7Xt8LoMGwuDfUyEaAJCvW6++Lbhe3TavfJ+Vnp4Ac2OZhqwo0K/5arStwXbbNGSWlo1wuWabacg0wlvLrNrfYFv1+Rttm/M1RvsYnABgtXr8ZEZb2hN68c5utSdjK305a8pC8uGmCfAl6amnntIHPvAB3X333Tp16pS2bt2qa665RjfffLO6u7vLx80U4J/JeaoNDg7qox/9qO6//37l83ldeOGFetOb3qS3v/3tsqyFtd4iwAcALDfPD3RysqBjY2GQfzpT1FjeUTpmq6slrtZEUzThAQBgSa2XgGS9o8vC+uJ5nq688sop2++9994Ff34DLBcGmC0+1690AagP/WsHA3h1+xttazSAwJPjNc3H6GhCpqFoEIFZHkxgW3Nct8IBCbZlyDLNaHtpUMFM62a4rbRumeWBCNXr5W116ww6ACAR4C+lNRPgr1UE+ACAlTSed3R8LK8TEwWN5hyNZIryA6krHVNnOi7L5D9sAIC1a7qQnrmz1wZCsPWFCnysJQw+Wn38qJtAdeg/c4eA8Lh81brj+vKjj+PDpgGBgkAqfUAfBJX1cHcQLgdSEB2rRut19y2fK9rp152ren/lHNH9o3NXHqf2XEHd45Xuq6D0nKaey/Urx6J5lIN+05BVFe6XBxLMcd2qurWqBihYU/YZ5UEOU7dNPWa6/QxAABYXAf7SIcBvcgT4AIBmUHR9DU/kdXy8ELbXzxQ1WXDVloypuyWuZIyKJQDA2jRT6FdC+Lc60WVh/eDnGGsR039gPfGDQL4fhvmeH8iLplio2Va1veFXg32uH8gPpt/m1j2GH1S2VR8b7vfl+2FHBz/QlG3hNUheabl8zpX+112f6rseWA0HFMw+IGC2AQg1Ax2iY2KWobhlyrYqyzE7HJhQWo5F+2LR4AgGHKBZEeAvnYXkw/TPBQBgnYjbprZ3pbWtM6XTmaKOjxd0arKgkVxRvzidVcwy1ZWOqT0Vk8l/KgAAa4hhmDp06JAkUbm7xjR6bUu3dFlYO+baSaN0y2uM1WIuobxhmIT3WBNMw5BpGbLXYO1AENQOLnD9QK4Xhv+l5dJggOp11/fllZcbrHt+5Xxnuj7jvvB6Vzs/kHwvkON5K30pc1IK86uD/anLU/fFbVO2WVmOWeE0CnFr6vLM52YQAbCaUIG/DKjABwA0q1zR0/HxvIYn8hrNOjqdKSrv+OpMx9SVjitu88EnAGDtYO7stYvq7LWLLgsAACy+6o4I4YACv9ylYOr6TAMRKgMD6rsg1C77Mx7j+ZVzTX+O2m4MOHO2GQX6tqm4FXYmKC3Hoo4CjZZL6qfrCKK5NfzqqTnqpt6YMuVG1RQg5SlCStN0KPzebDT1R/XUHOXjGl5T9X3Chemm95hyrqppSCTJkGQYkiEjvK1ejg6o7DPC40v3iQZLlGYuLRVLNTpf+TjDkFk+b9U5jbrl6IAp+xrcp3INleuuvo8kTRRctcQtvfu3L9Jzz+6Y6VsIZ4gKfAAAMC+puKXzNrbonO60Tk4WdHw8r5FMUaczRT1+alLpmK2udFwtCYtRugCAVS0IfPX339ZwX3//bYR9qxxdFtauoaH7Zwznp+vC0Nv7UqqWAQCYRk1HhFXYMbtR14PpBwfUDh4IuyNExwRzHVxQdS4vkOMHcjxfruer6AVyXF+O54fbS8ueL8eLjmuSeRbCjgyecs7q6FqA5fWGPeeu9CWgCgE+AACQZRra0p7UlvakxvOOhsfzGh4vaCznaHgiL388UFc6rs50XJZJkA8AWF1mq86m7fbaYBimDhw42PB1PnDgIK/tKtXb26u+vj4NDAxMOxCjPsTv6+sjvAcAYA0zDEO2YWi1NI70g3DgQCXYr4T7TjQIIBwM4Mtxo+1+1XLd8VPXp57LqRpc4PrhMcBMmFK1uRDgAwCAGu3JmNqTMe3obtHwRF7HxwsayxZ1OlvUI8MTak+G7fVTcVoNAwCaH3Nnrx90WVi79u/fr127dqmnZ8+0r2EpxKfyHgAANBvTMBS3jRWdqnLqIILZl0sDCqSg0nK9ro18bcv28IBS7U9t2/fq9apzlc5XdY7S+aW61vN1beSrW8Kr/prqHrN8LkNVbeqnbyvfeIqA+hb9jVv3l/69pfr2/uF9qqcIqLT3rz628X0aTxNQew3hY1dd9zT3UVA57uRkUa0JS2d3ps702wpLiAAfAAA0FLdNbe9Ka1tnSiNZR8fH8zo1WdBI1tHTo1nZpqmudEztqRgjNAEATWm2ubEbtd2WCPFXI7osrH1zCeUNwyS8BwAAaKAZBhGgOT1+MqMt7Qltakus9KWgCj+pAABgRoZhqLslrku2tmv3ud361W0des5ZbdrUGtd43tEjxyd1fDyvouuv9KUCAFBjrnNn79u3t3zMXXfdraGh+5f9WjF/0w3UuPfee6e8trfeequCgL9ZAAAAAADNiwAfAADMWSpu6byNLdp9brdecE6nLtnarp2b0pICPX5yUr84ndVk3i23bAIAYCWV5s6Wpob3JfUhPnNnry4zdVmwLKvhAA1CfAAAAABAM6OFPgAAOGOWaWhze1Kb25OayIft9U9OFDWSK+rERF7HxgN1pePqSMdkm4wXBACsHObOXtvm2mVBqp0qgdcaAAAAANCs+EQdAAAsSFsypgs3t2n3eV16/vZOPefsdm3rTCnv+vr58KR+OZpTtkhVPgBg5fT29s467zlzZ69OdFkAAAAAAKw1VOADAIBFEbNMbetM6eyOpEazjo6N53VqsqDRrKNnRnNyvEBx21TcMsPbquWYxZhCAAAwP3RZAAAAAACsJQT4AABgURmGoa6WuLpa4so7Xthef7KgvOOr6Poqup6KXqBs0dOoW5Tj+fJ9KVYX7ieidZtwHwAAzGIuoTxdFgAAAAAAqwEBPgAAWDLJmKVzN7To3A0tcj1feddX3vGqvsL1guurUA73/TDczxZVdH0FQRjuJxpU7xPuAwAAAAAAAADWEgJ8AACwLGzLVKtlqjUx9c8P1/OVqwn0w+Wc46nghBX7RddT0fWVKboayYbV/IFUCfWrw33blG0S7gPzNTg4OGMrakkKAl9DQ/dTzQoAAAAAAAAsIgJ8AACw4mzLVJtlqi05dZ/j+TXV+uVlNwr3XV9Fz5823E/YluK2oZhFuA/MxeHDhzUwMKB9+/bq0KFDDUP8IPB166236q677lZfX5/279+//BcKAAAAAAAArEEE+AAAoKnFLFOxGcL9XBTqF5xK0J9zvHLFfjncL7gayYTrklFVtW8oblvlCn7LNJb9OQLNYnBwUAMDA5Kku+66W5KmhPjV4b0kDQwMaNeuXVTiAwAAAFXoagUAAOaLAB8AAKxapXC/PRmbsq/ohlX6pXA/V1W9X3Q9FaJw33F9Tead8rpRCver2/JbphK2KZNwH2tcT88e7du3txzO14f49eG9JO3bt1c9PXtW5HoBAACAZkRXKwAAsBAE+AAAYE0qhfDThfs5J2zBX2rHXwr3C44XVu17voqOr4m8U67kN42qVvxRqF9aJtzHWmAYpg4dOiRJU0L8AwcOqr//tinh/XQfSAIAAADrEV2tAADAQhHgAwCAdacU7is1NdwvuJUgP1cK+Ett+l1PRS+Q44Zt+cdLlfuuJ8usq9q3TaVilmIWwSZWl+lC/OrgXiK8BwAAABqhqxUAAFgoAnwAAIAqCdtSwramhPtBEKjo+coXayv268P9YhToj2ZdPVv0ZBiGkjFLqZgZ3VqyCfXR5BqF+NUI7wEAAIDG6GoFAAAWygiCIFjpi1jrdu/eLUk6evToCl8JAABYCkEQqOD6KkTt+HNFT9mip0zRVbboKl/0VIja9ueiUD8Vs8qBfjJmEuqjKXmepyuvvHLK9nvvvVeWZa3AFQEAAACrQ6NK+3qE9wCAlfb4yYy2tCf04p3dDacixfwtJB+mAh8AAGCBSlX2yZilDtX+oZt3PE0WXGUKriYLrrJFrxzq5x1fpzIF5R1PZtU5UjFLybgp2+RDHKycIPDV339bw339/bfxQSMAAAAwA7paAQCA+SLABwAAWEKlUH5ja0JSWK2fd/wozHejcN9TznGVK4bt+E9mHBVG/XKon4pXgn3LNFb4GWE9mK1aqH4eTwAAAABTGYapAwcONvy7+sCBg/wtDQAAGiLABwAAWEaGYSgVD0N5aWqoX12pnyu65bb7J/KOCq4v2zSqWu+HX4T6WEyNwvt9+/ZOma+TEB8AAACYGV2tAADAfBDgAwAArLDqUH9TWyXUz5Xb73vlYL/geOVQf7wc6ptRoG+Ww32TUB/zMF14X/pgsb4FKCE+AAAA0BhdrQAAwHwR4AMAADQhwzCUjttKx22pLdwWBIGyxUqYnyl4yhRd5aNQPx+F+nnHU8yyyqF+Km4paRPqY3ZDQ/dPG95LjefxvOuuu9Xb+1L19vYu/wUDAAAATYiuVgAAYCEI8AEAAFYJwzDUkrDVkrC1Odrm+2GlfnWoP1lwlHf8crA/PhZW6sdss6r9frhsGoT6qOjt7VVfX58GBgamhPcl9SF+X18f4T0AAAAQoasVAABYKAJ8AACAVcw0G4f62ZpQP/zKRaF+3vE0li0q7/qK26X2+4T6CO3fv1+7du1ST8+eaT9ALH3wSOU9AAAAUIuuVgAAYKEI8AEAANYY0zTUmrDVmrC1Jdrm+4EyxVKFfhjoZwuucm6lUn80W1ShLtRPxSwlYiah/jozlw8ODcPkA0YAAACgDl2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| |
| "text/plain": [ | |
| "<Figure size 2016x576 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots(figsize=(14, 4), dpi=144, layout='constrained')\n", | |
| "t_grid = t_values.get_value()\n", | |
| "ax.scatter(t_grid, data, marker='x', c='k')\n", | |
| "\n", | |
| "mu = idata.posterior_predictive.mean(dim=['chain', 'draw']).obs\n", | |
| "hdi = pm.hdi(idata.posterior_predictive.obs).obs\n", | |
| "ax.plot(t_grid, mu.values)\n", | |
| "ax.fill_between(t_grid, *hdi.values.T, alpha=0.25, color='tab:blue')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "7b853671", | |
| "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": "3.13.5" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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