25. Optimization of a dynamical system.ipynb

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    "Step 19 (Speical Topic 3): Optimization of Dynamical Systems\n",
    "----\n",
    "***\n",
    "\n",
    "In this step, we integrate a forward Partial Differential Equation (PDE) solver with an optimization algorithm to fine-tune input parameters, ensuring that the solver's output aligns with specified target values. Utilizing [Automatic Differentiation](https://jax.readthedocs.io/en/latest/jax-101/04-advanced-autodiff.html) in JAX, we can effortlessly compute derivatives of the model output with respect to the input parameters. This capability facilitates the use of gradient-based optimization algorithms, such as the gradient descent method, for efficient exploration of the parameter space. While this step employs an Ordinary Differential Equation (ODE) as the forward solver, the optimization framework is versatile and can be applied to other ODE and PDE solvers."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7ffed498",
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   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as np\n",
    "from jax import linear_util as lu\n",
    "from jax.flatten_util import ravel_pytree\n",
    "import numpy as onp\n",
    "from functools import partial\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as opt\n",
    "import sys"
   ]
  },
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   "cell_type": "markdown",
   "id": "3342765d",
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   "source": [
    "\n",
    "A brief explanation has been given below about what this program does.\n",
    "\n",
    "Define a Dynamical System: It sets up a mathematical model that describes how a dynamical system (specifically, the Lorenz system) evolves over time. This model involves equations that govern how the system's variables change with time.\n",
    "\n",
    "Numerical Integration: It uses a numerical method (Runge-Kutta 4th order) to simulate the behavior of the dynamical system over a range of time points. This involves repeatedly applying the equations from the dynamical system to calculate how the system's variables change at each time step.\n",
    "\n",
    "Gradient Computation: It calculates how sensitive the system's behavior is to changes in its parameters. This is important for understanding how small adjustments to certain parameters affect the system's output. The program computes these gradients using different methods, including finite differences and automatic differentiation.\n",
    "\n",
    "Optimization: It tries to find the best-fitting parameters for the dynamical system by minimizing the difference between the system's behavior and a target state. In other words, it adjusts the parameters to make the simulated system's output as close as possible to the desired outcome.\n",
    "\n",
    "Printing Results: The program then prints out the estimated parameters that make the model fit the target state most closely. It also shows the initial parameters and the ground truth parameters for comparison.\n",
    "\n",
    "In simple terms, this program simulates a dynamic system, like weather patterns or fluid flow, and tries to figure out the rules that govern it. It does this by adjusting parameters in a mathematical model until the model's predictions match real-world observations as closely as possible.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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   "cell_type": "markdown",
   "id": "112ed679",
   "metadata": {},
   "source": [
    "### Define dynamical system"
   ]
  },
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   "source": [
    "#### Lorenz System\n",
    "The Lorenz system was initially derived from a Oberbeck-Boussinesq approximation. This approximation is\n",
    "a coupling of the Navier-Stokes equations with thermal convection. The original problem was a 2D problem\n",
    "considering the thermal convection between two parallel horizontal plates. The Lorenz system arises from\n",
    "using a truncated Fourier-Galerkin expansion.\n",
    "\n",
    "$$\\frac{dx}{dt}=\\sigma(y-x),$$ \n",
    "$$\\frac{dy}{dt}=x(\\rho-z)-y,$$ \n",
    "$$\\frac{dz}{dt}=xy-\\beta z ,$$ <br>\n",
    ">where,\n",
    "$\\sigma \\,$ is the Prandle number\\, \n",
    "$\\rho \\, $ is a scaled value of Rayleigh number and $\\beta \\,$ is an aspect ratio \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "id": "93df0812",
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   "source": [
    "def Lorenz_rhs_func(state, t, ode_params):\n",
    "    rho, sigma, beta = ode_params\n",
    "    x, y, z = state\n",
    "    return np.array([sigma * (y - x), x * (rho - z) - y, x * y - beta * z])"
   ]
  },
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   "cell_type": "markdown",
   "id": "99e140e6",
   "metadata": {},
   "source": [
    "### Runge-Kutta Method\n",
    "RK method is widely used for solving initial value problems of differential equation by constructing higher order approximation of a differential problem. 4th order variant, or RK4 produces more accurate result than other simpler numerical methods.\n",
    "\n",
    "In the code, h is the small time step, $k_1$ is the slope at the initial value, derived simply from euler's method.\n",
    " $k_2$ and $k_3$ both are slope at midpoint of the interval h, but using $k_1$ and $k_2$ respectively for calculating. And $k_4$ is the slope at the end-point. Weighted average of these 4 slopes is used to calculate a more accurate estimation of the endpoint.\n"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "id": "dbbccd42",
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   "outputs": [],
   "source": [
    "# About the decorator: f is a function (not JAX array) and JAX needs to know that so we specify it as \"static\"\n",
    "@partial(jax.jit, static_argnums=(2,))\n",
    "def rk4(state, t_crt, f, ode_params):\n",
    "    y_prev, t_prev = state\n",
    "    h = t_crt - t_prev\n",
    "    k1 = h * f(y_prev, t_prev, ode_params)\n",
    "    k2 = h * f(y_prev + k1/2., t_prev + h/2., ode_params)\n",
    "    k3 = h * f(y_prev + k2/2., t_prev + h/2., ode_params)\n",
    "    k4 = h * f(y_prev + k3, t_prev + h, ode_params)\n",
    "    y_crt = y_prev + 1./6 * (k1 + 2 * k2 + 2 * k3 + k4)\n",
    "    return (y_crt, t_crt), y_crt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "38413e02",
   "metadata": {},
   "outputs": [],
   "source": [
    "#ys_ = odeint(rk4, Lorenz_rhs_func, y0, ts, ode_params_opt)\n",
    "\n",
    "#stepper is the interative solver, here it is RK4 method\n",
    "#f is funcition to operate; here which is Lorenz function\n",
    "#ts = np.arange(0, 101*dt, dt)\n",
    "#rho, sigma, beta = ode_params\n",
    "#odeint takes system function, ode parameters as input and calculates space values of the system at progressing small time difference\n",
    "def odeint(stepper, f, y0, ts, ode_params):\n",
    "\n",
    "    def stepper_partial(state, t_crt):\n",
    "        #stepper function is used to advance the state of an ODE system from one time point to another. Output contains new state, new time\n",
    "        return stepper(state, t_crt, f, ode_params)\n",
    "\n",
    "    ys = []\n",
    "    state = (y0, ts[0])\n",
    "    for (i, t_crt) in enumerate(ts[1:]):\n",
    "        state, y = stepper_partial(state, t_crt)\n",
    "        #print(\"state, y\", state, y)\n",
    "        ys.append(y)\n",
    "    ys = np.array(ys)\n",
    "    #print(\"ys =\", ys)\n",
    "    return ys"
   ]
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   "execution_count": 5,
   "id": "330404e9",
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     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#print(\"dumba\")\n",
    "y0 = np.array([1., 1., 1.])\n",
    "dt = 1e-2\n",
    "ts = np.arange(0, 101*dt, dt) # ts defined for optimization\n",
    "#ts_plot = np.arange(0, 5001*dt, dt) # ts defined for visulization here\n",
    "ode_params_gt = [28., 10., 8./3.]\n",
    "\n",
    "ys_gt_ = odeint(rk4, Lorenz_rhs_func, y0, ts, ode_params_gt)\n",
    "\n",
    "ys_gt = np.vstack((y0[None, ...], ys_gt_))\n",
    "#ys_gt is the array consisting the states or space value over time of Lorenz System\n",
    "fig = plt.figure(figsize=(6, 4), dpi=150)\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "x0, x1, x2 = ys_gt.T\n",
    "ax.plot(x0, x1, x2, lw=0.5, color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29efa401",
   "metadata": {},
   "source": [
    "### Compute derivatives with several methods"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cca6dd25",
   "metadata": {},
   "source": [
    "#### Finite Difference Based Gradient Computing Function\n",
    "\n",
    "$$\\frac{d}{dt}f(x)=\\lim_{h \\to 0} \\frac{f(x+h)-f(x-h)}{2h} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a3fc8ff6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient_fd(ys, ts, obj_func, state_rhs_func, ode_params):\n",
    "    print(f\"running finite difference\")\n",
    "    \n",
    "    y0 = ys[0]\n",
    "    h = 1e-1\n",
    "    ode_params_flat, unravel = ravel_pytree(ode_params)\n",
    "\n",
    "    grads = []\n",
    "    for i in range(len(ode_params_flat)):\n",
    "        ode_params_flat_plus = ode_params_flat.at[i].add(h)\n",
    "        ys_plus_ = odeint(rk4, state_rhs_func, y0, ts, unravel(ode_params_flat_plus))\n",
    "        tau_plus = obj_func(ys_plus_[-1])\n",
    "           \n",
    "        ode_params_flat_minus = ode_params_flat.at[i].add(-h)\n",
    "        ys_minus_ = odeint(rk4, state_rhs_func, y0, ts, unravel(ode_params_flat_minus))\n",
    "        tau_minus = obj_func(ys_minus_[-1])\n",
    "        \n",
    "        grad = (tau_plus - tau_minus) / (2 * h)\n",
    "        grads.append(grad)\n",
    "\n",
    "    grads = unravel(np.array(grads))\n",
    "\n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "28c3b707",
   "metadata": {},
   "outputs": [],
   "source": [
    "# a = 1,2,3\n",
    "# print(a)\n",
    "# b, unravel = ravel_pytree(a)\n",
    "# print(b)\n",
    "# c = unravel(b)\n",
    "# print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e04af9",
   "metadata": {},
   "source": [
    "#### Automatic Differentiation\n",
    "\n",
    "In automatic differentiation (AD), numerical methods like finite differences are not used for calculating derivatives in each step. Instead, AD relies on symbolic manipulation or dual numbers to compute exact derivatives. This is one of the fundamental differences between AD and numerical differentiation methods, such as finite differences.\n",
    "\n",
    "Here's a brief explanation of how derivatives are calculated in each step of AD without numerical approximation:\n",
    "\n",
    "Symbolic Manipulation: In the forward and reverse modes of AD, derivatives are calculated symbolically, not numerically. This means that the elementary operations used to compute the derivative are represented in terms of their symbolic derivatives. \n",
    "\n",
    "Dual Numbers: Dual numbers are an extension of real numbers that include an infinitesimal component (ε). In AD, dual numbers are used to simultaneously track the function value and its derivative. For example, if x is a dual number representing a variable, it might be written as x = a + ε * b, where a is the function value, and b is its derivative with respect to x. As you perform operations on dual numbers, AD updates both the function value and its derivative using the rules of elementary calculus.\n",
    "\n",
    "Chain Rule: AD applies the chain rule systematically during the calculation of derivatives. When you have a composite function, AD knows how to combine the derivatives of elementary operations using the chain rule to compute the derivative of the entire function.\n",
    "\n",
    "By working symbolically with dual numbers and using the chain rule, AD can compute derivatives accurately and efficiently without the need for numerical approximations. This allows it to calculate derivatives at each step of the computation, providing exact gradients or derivatives rather than approximations that would be obtained through numerical methods like finite differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "25ff04e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient_ad_diff_through_loops(ys, ts, obj_func, state_rhs_func, ode_params):\n",
    "    print(f\"running autodiff, differentiate through loops\")\n",
    "\n",
    "    y0 = ys[0]\n",
    "    def func(ode_params):\n",
    "        ys_ = odeint(rk4, state_rhs_func, y0, ts, ode_params)\n",
    "        return obj_func(ys_[-1])\n",
    "\n",
    "    #jax.grad(FUNCTION) is afunction fron jax library which is used for differentiating \"FUNCTION\" using automatic differentiation\n",
    "    grad_func = jax.grad(func)\n",
    "    grads = grad_func(ode_params)\n",
    "    \n",
    "    return grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7f485cca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running finite difference\n",
      "grads = [Array(-7.501421, dtype=float32), Array(16.432524, dtype=float32), Array(-102.63889, dtype=float32)]\n",
      "\n",
      "running autodiff, differentiate through loops\n",
      "grads = [Array(-7.498921, dtype=float32, weak_type=True), Array(16.436684, dtype=float32, weak_type=True), Array(-102.749664, dtype=float32, weak_type=True)]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "def obj_func(yf, target_yf):\n",
    "    return np.sum((yf - target_yf)**2)\n",
    "\n",
    "target_yf = ys_gt_[-1]\n",
    "obj_func_partial = lambda yf: obj_func(yf, target_yf)\n",
    "\n",
    "# ode_params_0 = [np.array([26., 8., 2.])]\n",
    "ode_params_0 = [26., 8., 2.]\n",
    "\n",
    "ys_ = odeint(rk4, Lorenz_rhs_func, y0, ts, ode_params_0)\n",
    "ys = np.vstack((y0[None, ...], ys_))\n",
    "\n",
    "\n",
    "grads_fd = compute_gradient_fd(ys, ts, obj_func_partial, Lorenz_rhs_func, ode_params_0)\n",
    "print(f\"grads = {grads_fd}\\n\")\n",
    "\n",
    "grads_ad_diff_through_loops = compute_gradient_ad_diff_through_loops(ys, ts, obj_func_partial, Lorenz_rhs_func, ode_params_0)\n",
    "print(f\"grads = {grads_ad_diff_through_loops}\\n\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6cff690",
   "metadata": {},
   "source": [
    "The case study above demonstrates that both finite difference methods and automatic differentiation (autodiff) yield approximately similar results. In our next simplified example, we will illustrate how autodiff not only achieves greater accuracy but also proves to be more efficient than the finite difference method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "742f9b8b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.21 ms ± 26.3 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "[2.50000000e-01 1.96611933e-01 1.04993585e-01 4.51766597e-02\n",
      " 1.76627062e-02 6.64805667e-03 2.46650929e-03 9.10221180e-04\n",
      " 3.35237671e-04 1.23379350e-04 4.53958077e-05 1.67011429e-05\n",
      " 6.14413685e-06 2.26031919e-06 8.31527336e-07 3.05902133e-07\n",
      " 1.12535149e-07 4.13993738e-08 1.52299793e-08 5.60279637e-09\n",
      " 2.06115361e-09 7.58256042e-10 2.78946809e-10 1.02618796e-10\n",
      " 3.77513454e-11 1.38879439e-11 5.10908903e-12 1.87952882e-12\n",
      " 6.91440011e-13 2.54366565e-13 9.35762297e-14 3.44247711e-14\n",
      " 1.26641655e-14 4.65888615e-15 1.71390843e-15 6.30511676e-16\n",
      " 2.31952283e-16 8.53304763e-17 3.13913279e-17 1.15482242e-17\n",
      " 4.24835426e-18 1.56288219e-18 5.74952226e-19 2.11513104e-19\n",
      " 7.78113224e-20 2.86251858e-20 1.05306174e-20 3.87399763e-21\n",
      " 1.42516408e-21 5.24288566e-22 1.92874985e-22 7.09547416e-23\n",
      " 2.61027907e-23 9.60268005e-24 3.53262857e-24 1.29958143e-24\n",
      " 4.78089288e-25 1.75879220e-25 6.47023493e-26 2.38026641e-26\n",
      " 8.75651076e-27 3.22134029e-27 1.18506486e-27 4.35961000e-28\n",
      " 1.60381089e-28 5.90009054e-29 2.17052201e-29 7.98490425e-30\n",
      " 2.93748211e-30 1.08063928e-30 3.97544974e-31 1.46248623e-31\n",
      " 5.38018616e-32 1.97925988e-32 7.28129018e-33 2.67863696e-33\n",
      " 9.85415469e-34 3.62514092e-34 1.33361482e-34 4.90609473e-35\n",
      " 1.80485139e-35 6.63967720e-36 2.44260074e-36 8.98582594e-37\n",
      " 3.30570063e-37 1.21609930e-37 4.47377931e-38 1.64581143e-38\n",
      " 6.05460190e-39 2.22736356e-39 8.19401262e-40 3.01440879e-40\n",
      " 1.10893902e-40 4.07955867e-41 1.50078576e-41 5.52108228e-42\n",
      " 2.03109266e-42 7.47197234e-43 2.74878501e-43 1.01122149e-43]\n"
     ]
    }
   ],
   "source": [
    "from numpy.matrixlib import defmatrix\n",
    "from jax.config import config\n",
    "config.update(\"jax_enable_x64\", True)\n",
    "\n",
    "def sum_logistic(x):\n",
    "  return np.sum(1.0 / (1.0 + np.exp(-x)))\n",
    "\n",
    "x_small = np.arange(100.)\n",
    "#y_small = np.linspace(0,3,100)\n",
    "\n",
    "derivative_fn = jax.grad(sum_logistic)  # define a function which is the gradient of sum_logistic\n",
    "%timeit derivative_fn(x_small)\n",
    "print(derivative_fn(x_small))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c2bfd762",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.2 ms ± 319 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "[2.49999999e-01 1.96611936e-01 1.04993582e-01 4.51766624e-02\n",
      " 1.76626997e-02 6.64805810e-03 2.46650700e-03 9.10219455e-04\n",
      " 3.35241168e-04 1.23378641e-04 4.53965754e-05 1.66977543e-05\n",
      " 6.14619466e-06 2.25952590e-06 8.31335001e-07 3.05533376e-07\n",
      " 1.13686838e-07 4.26325641e-08 1.42108547e-08 7.10542736e-09\n",
      " 7.10542736e-09 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "def first_finite_differences(f, x):\n",
    "  eps = 1e-6\n",
    "  return np.array([(f(x + eps * v) - f(x - eps * v)) / (2 * eps)\n",
    "                   for v in np.eye(len(x))])\n",
    "\n",
    "%timeit first_finite_differences(sum_logistic, x_small)\n",
    "print(first_finite_differences(sum_logistic, x_small))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bbe03ee",
   "metadata": {},
   "source": [
    "### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7631f711",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "## optimize(ode_params_0, y0, ts, obj_func_partial, Lorenz_rhs_func, bounds, compute_gradient_fd)\n",
    "\n",
    "def optimize(ode_params_0, y0, ts, obj_func, state_rhs_func, bounds, compute_gradient_func):\n",
    "    x_ini, unravel = ravel_pytree(ode_params_0)\n",
    "    obj_vals = []\n",
    "\n",
    "    def objective(x):\n",
    "        print(f\"\\n######################### Evaluating objective value - step {objective.counter}\")\n",
    "        x = np.array(x)\n",
    "        ode_params = unravel(x)\n",
    "        ys_ = odeint(rk4, state_rhs_func, y0, ts, ode_params)\n",
    "        ys = np.vstack((y0[None, ...], ys_))\n",
    "        obj_val = obj_func(ys[-1])\n",
    "\n",
    "        objective.ode_params = ode_params\n",
    "        objective.ys = ys\n",
    "        objective.x = ode_params\n",
    "\n",
    "        objective.counter += 1\n",
    "        obj_vals.append(obj_val)\n",
    "\n",
    "        print(f\"obj_val = {obj_val}\")\n",
    "        print(f\"ode_params = {ode_params}\")\n",
    "        print(f\"ys[-1] = {ys[-1]}\")\n",
    "\n",
    "        return obj_val\n",
    "\n",
    "    def derivative(x):\n",
    "        ode_params = objective.ode_params\n",
    "        ys = objective.ys\n",
    "\n",
    "        grads = compute_gradient_func(ys, ts, obj_func, state_rhs_func, ode_params)\n",
    "        print(f\"########################################################\")\n",
    "        print(f\"grads = {grads}\")\n",
    "        print(f\"########################################################\")\n",
    "\n",
    "        grads_ravelled, _ = ravel_pytree(grads)\n",
    "        # 'L-BFGS-B' requires the following conversion, otherwise we get an error message saying\n",
    "        # -- input not fortran contiguous -- expected elsize=8 but got 4\n",
    "        return onp.array(grads_ravelled, order='F', dtype=onp.float64)\n",
    "\n",
    "    objective.counter = 0\n",
    "    options = {'maxiter': 1000, 'disp': True}  # CG or L-BFGS-B or Newton-CG or SLSQP\n",
    "    res = opt.minimize(fun=objective,\n",
    "                       x0=x_ini,\n",
    "                       method='SLSQP',\n",
    "                       jac=derivative,\n",
    "                       bounds=bounds,\n",
    "                       callback=None,\n",
    "                       options=options)\n",
    "        \n",
    "    return objective.x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa2d33e",
   "metadata": {},
   "source": [
    "### Solving the inverse problem using Finite Difference Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3e8e1d4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "######################### Evaluating objective value - step 0\n",
      "obj_val = 4.860941287589725\n",
      "ode_params = [Array(26., dtype=float64), Array(8., dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-10.52796043 -10.17111714  28.86326064]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(-6.92301708, dtype=float64), Array(-5.14942292, dtype=float64), Array(18.96074537, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 1\n",
      "obj_val = 4.410157956860218\n",
      "ode_params = [Array(30., dtype=float64), Array(12., dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.98216602 -9.483049   31.02914495]\n",
      "\n",
      "######################### Evaluating objective value - step 2\n",
      "obj_val = 4.5308537838420157e-05\n",
      "ode_params = [Array(28.01884586, dtype=float64), Array(10.01884586, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37604064 -8.36218931 29.36591822]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(-0.00014405, dtype=float64), Array(0.00261211, dtype=float64), Array(-0.55425541, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 3\n",
      "obj_val = 4.3328425968302456e-05\n",
      "ode_params = [Array(28.01976363, dtype=float64), Array(10.01664552, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37537389 -8.36062631 29.36688514]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(0.00207508, dtype=float64), Array(5.73364305e-05, dtype=float64), Array(-0.53331802, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 4\n",
      "obj_val = 4.106380298681398e-05\n",
      "ode_params = [Array(28.01908555, dtype=float64), Array(10.01675259, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37560073 -8.36089563 29.36655643]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(0.00147836, dtype=float64), Array(0.00061734, dtype=float64), Array(-0.53849249, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 5\n",
      "obj_val = 3.2963945786474016e-05\n",
      "ode_params = [Array(28.01660262, dtype=float64), Array(10.01577886, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37619325 -8.36108683 29.3657001 ]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(0.00022877, dtype=float64), Array(0.00147527, dtype=float64), Array(-0.54818684, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 6\n",
      "obj_val = 2.2305330989485424e-05\n",
      "ode_params = [Array(28.01328149, dtype=float64), Array(10.01327813, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37677993 -8.36064907 29.36486189]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(-0.00062246, dtype=float64), Array(0.00158433, dtype=float64), Array(-0.55303034, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 7\n",
      "obj_val = 1.3800534692919301e-05\n",
      "ode_params = [Array(28.01067905, dtype=float64), Array(10.01033877, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37707385 -8.35974055 29.36446013]\n",
      "running finite difference\n",
      "########################################################\n",
      "grads = [Array(-0.00061286, dtype=float64), Array(0.0008233, dtype=float64), Array(-0.55015333, dtype=float64)]\n",
      "########################################################\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3800534692919301e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 8\n",
      "            Gradient evaluations: 7\n",
      "\n",
      "Ground truth parameter values = [28.0, 10.0, 2.6666666666666665]\n",
      "Ground truth yf = [-9.378615  -8.3570595 29.362402 ]\n",
      "\n",
      "Initial parameter values = [26.0, 8.0, 2.0]\n",
      "Optimized parameter values = [Array(28.01067905, dtype=float64), Array(10.01033877, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "Optimized yf = [-9.37707385 -8.35974055 29.36446013]\n"
     ]
    }
   ],
   "source": [
    "#just some arrays containing two variables, probably x, y space value, let's see\n",
    "\n",
    "bounds = np.array([[26., 30.], [8., 12.], [8./3., 8./3.]])\n",
    "\n",
    "#calling the main optimizing function, let's go to optimize function, it takes 7 input arguments\n",
    "\n",
    "\n",
    "ode_params_opt = optimize(ode_params_0, y0, ts, obj_func_partial, Lorenz_rhs_func, bounds, compute_gradient_fd)\n",
    "\n",
    "\n",
    "\n",
    "#optimized ode paramaters derived from optimize function would be an inpur argument of odeint function\n",
    "\n",
    "ys_ = odeint(rk4, Lorenz_rhs_func, y0, ts, ode_params_opt)\n",
    "\n",
    "print(f\"\\nGround truth parameter values = {ode_params_gt}\")\n",
    "print(f\"Ground truth yf = {target_yf}\")\n",
    "print(f\"\\nInitial parameter values = {ode_params_0}\")\n",
    "print(f\"Optimized parameter values = {ode_params_opt}\")\n",
    "print(f\"Optimized yf = {ys_[-1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47c106db",
   "metadata": {},
   "source": [
    "### Solving the inverse problem using Automatic Differentiation Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "172fabdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "######################### Evaluating objective value - step 0\n",
      "obj_val = 4.860941287589725\n",
      "ode_params = [Array(26., dtype=float64), Array(8., dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-10.52796043 -10.17111714  28.86326064]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(-6.91298213, dtype=float64), Array(-5.130735, dtype=float64), Array(19.05076497, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 1\n",
      "obj_val = 4.410157956860218\n",
      "ode_params = [Array(30., dtype=float64), Array(12., dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.98216602 -9.483049   31.02914495]\n",
      "\n",
      "######################### Evaluating objective value - step 2\n",
      "obj_val = 4.5530123214976924e-05\n",
      "ode_params = [Array(28.01889123, dtype=float64), Array(10.01889123, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37603467 -8.36220193 29.36592691]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(0.0015845, dtype=float64), Array(0.00330562, dtype=float64), Array(-0.00253483, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 3\n",
      "obj_val = 4.1048447656296876e-05\n",
      "ode_params = [Array(28.01911315, dtype=float64), Array(10.01666937, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.37557771 -8.36083868 29.36658988]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(0.00328236, dtype=float64), Array(0.00121416, dtype=float64), Array(0.01374493, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 4\n",
      "obj_val = 3.360539721002528e-05\n",
      "ode_params = [Array(28.01746655, dtype=float64), Array(10.01439108, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.3756862  -8.3600138  29.36643895]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(0.00358246, dtype=float64), Array(0.00035915, dtype=float64), Array(0.01818499, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 5\n",
      "obj_val = 5.834839648128331e-06\n",
      "ode_params = [Array(28.00678528, dtype=float64), Array(10.00410361, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.3772091  -8.35732328 29.36434815]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(0.00243928, dtype=float64), Array(-0.00119133, dtype=float64), Array(0.01707735, dtype=float64)]\n",
      "########################################################\n",
      "\n",
      "######################### Evaluating objective value - step 6\n",
      "obj_val = 2.3090861427081626e-07\n",
      "ode_params = [Array(28.00056728, dtype=float64), Array(9.99978854, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "ys[-1] = [-9.3784044  -8.35675983 29.36271278]\n",
      "running autodiff, differentiate through loops\n",
      "########################################################\n",
      "grads = [Array(0.0005957, dtype=float64), Array(-0.00058269, dtype=float64), Array(0.00519343, dtype=float64)]\n",
      "########################################################\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3090861427081626e-07\n",
      "            Iterations: 6\n",
      "            Function evaluations: 7\n",
      "            Gradient evaluations: 6\n",
      "\n",
      "Ground truth parameter values = [28.0, 10.0, 2.6666666666666665]\n",
      "Ground truth yf = [-9.378615  -8.3570595 29.362402 ]\n",
      "\n",
      "Initial parameter values = [26.0, 8.0, 2.0]\n",
      "Optimized parameter values = [Array(28.00056728, dtype=float64), Array(9.99978854, dtype=float64), Array(2.66666667, dtype=float64)]\n",
      "Optimized yf = [-9.3784044  -8.35675983 29.36271278]\n"
     ]
    }
   ],
   "source": [
    "#just some arrays containing two variables, probably x, y space value, let's see\n",
    "\n",
    "bounds = np.array([[26., 30.], [8., 12.], [8./3., 8./3.]])\n",
    "\n",
    "#calling the main optimizing function, let's go to optimize function, it takes 7 input arguments\n",
    "\n",
    "\n",
    "ode_params_opt = optimize(ode_params_0, y0, ts, obj_func_partial, Lorenz_rhs_func, bounds, compute_gradient_ad_diff_through_loops)\n",
    "\n",
    "\n",
    "\n",
    "#optimized ode paramaters derived from optimize function would be an inpur argument of odeint function\n",
    "\n",
    "ys_ = odeint(rk4, Lorenz_rhs_func, y0, ts, ode_params_opt)\n",
    "\n",
    "print(f\"\\nGround truth parameter values = {ode_params_gt}\")\n",
    "print(f\"Ground truth yf = {target_yf}\")\n",
    "print(f\"\\nInitial parameter values = {ode_params_0}\")\n",
    "print(f\"Optimized parameter values = {ode_params_opt}\")\n",
    "print(f\"Optimized yf = {ys_[-1]}\")"
   ]
  }
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