{ "cells": [ { "cell_type": "markdown", "id": "13aec53b-1a81-4ce7-9d33-e5d14a21da4d", "metadata": {}, "source": [ "# Appendix C: Numerical solutions of ODES\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "id": "c0b00d65-a6ef-4351-9d67-ee149a3ac355", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "
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\\n\"+\n", " \"

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\\n\"+\n \"

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\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n const el = document.getElementById(\"p1001\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.0.min.js\"];\n const css_urls = [];\n\n const inline_js = [ function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\nfunction(Bokeh) {\n }\n ];\n\n function run_inline_js() {\n if (root.Bokeh !== undefined || force === true) {\n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\nif (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"p1001\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import scipy.integrate\n", "import scipy.optimize\n", "\n", "import bokeh.io\n", "import bokeh.plotting\n", "\n", "bokeh.io.output_notebook()" ] }, { "cell_type": "markdown", "id": "e7ea1984-4349-466a-991d-b5e467b04e66", "metadata": {}, "source": [ "
\n", "\n", "In [Technical Appendix 2a](../technical_appendices/02a_numerical_odes.ipynb), we learned basic syntax of how to use `scipy.integrate.odeint()` to perform numerical integration of ordinary differential equations. We gave a cursory description of how it works, but the integration was more or less treated like a black box. Here, we give a more pedagogical introduction to how numerical solution of systems of ODEs works and why it is necessary to use a package like `scipy.integrate.odeint()`. \n", "\n", "In our examples, we mostly use dynamical equations for chemical kinetics. Many of the dynamical equations we encounter in the study of biological circuits are equations describing chemical kinetics or are otherwise similar with similar issues." ] }, { "cell_type": "markdown", "id": "8659423c-626f-4d11-bfac-ab1d078c6b69", "metadata": {}, "source": [ "## Euler's method as an introduction to numerical methods\n", "\n", "A classic introduction to numerical methods for solving system of time-based ODEs involves **Euler's method**. Consider an ordinary differential equation\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = f(y, t),\n", "\\end{align}\n", "\n", "with initial condition $y(0) = y_0$. Our goal is to find $y(t)$. For some functions $f(y, t)$, and analytical solution can be found. For example, if $f = -k y$, we have exponential decay and $y(t) = y_0\\mathrm{e}^{-kt}$. But we cannot always find an analytical solution.\n", "\n", "Our goal instead is to try to find $y(t)$ *at discrete time points*. For Euler's method in particular, we will chose time points $t = \\{0, \\Delta t, 2\\Delta t, \\ldots n\\Delta t\\}$, where $\\Delta t$ is some small time step.\n", "\n", "Recalling your first forays into calculus, recall one of the definitions of a derivative,\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = \\lim_{\\Delta t\\to0}\\frac{y(t+\\Delta t) - y(t)}{\\Delta t}.\n", "\\end{align}\n", "\n", "We will drop the limit part, but keep $\\Delta t$ small, giving us\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}y}{\\mathrm{d}t} \\approx \\frac{y(t+\\Delta t) - y(t)}{\\Delta t}.\n", "\\end{align}\n", "\n", "This expression for the time derivative of $y$ is referred to as **the forward differencing formula**. Inserting this into $\\mathrm{d}y/\\mathrm{d}t = f(y, t)$ and rearranging, we have\n", "\n", "\\begin{align}\n", "y(t+\\Delta t) \\approx y(t) + \\Delta t f(y(t), t).\n", "\\end{align}\n", "\n", "This is a nice formula, because if we start at time $t = 0$, we know $y(0) = y_0$, so we can solve for $y(\\Delta t)$ as\n", "\n", "\\begin{align}\n", "y(\\Delta t) \\approx y_0 + \\Delta t f(y_0, 0).\n", "\\end{align}\n", "\n", "But now that we have $y(\\Delta t)$, we can use the formula again to get $y(2\\Delta t)$.\n", "\n", "\\begin{align}\n", "y(2\\Delta t) \\approx y(\\Delta t) + \\Delta t f(y(\\Delta t), \\Delta t).\n", "\\end{align}\n", "\n", "And we can keep marching forward in time until we get $y$ at all of the desired time points. This technique is more or less how initial value problems are solved. Starting from an initial condition, we use a differencing formula to figure out what the value of the solution to the ODE(s) is at a time point a little bit in the future. We then keep marching forward in time.\n", "\n", "Euler's method is an example of an **explicit** technique for solving ODEs, since the value of the solution at time $t + \\Delta t$ depends only on the right-hand side evalued at time $t$. That is, $y(t + \\Delta t)$ depends only on $f(y, t)$. We will contrast this with **implicit** methods later.\n", "\n", "Now, we can code up Euler's method. We will assume vectorial $y$, meaning that we are solving a *system* of ODEs. There are no additional considerations for a vectorial $y$. In the function, note that the keyword argument `args` is a tuple that gives extra parameters that are passed into the function `f`." ] }, { "cell_type": "code", "execution_count": 2, "id": "03f7b751-e282-4378-a3fe-52366f3a8ee3", "metadata": {}, "outputs": [], "source": [ "def solve_euler(f, y0, t_max, delta_t, args=()):\n", " \"\"\"Solve an ODE defined by y'(t) = f(y, t, *args)\n", " using Euler's method.\"\"\"\n", " # Initialize output array\n", " y = np.empty((int(t_max / delta_t) + 1, len(y0)))\n", " \n", " # Insert initial condition\n", " y[0] = y0\n", "\n", " # Start at t = 0, with index 0\n", " t = 0.0\n", " i = 0\n", " \n", " # March forward in time\n", " while i < len(y) - 1:\n", " y[i+1] = y[i] + delta_t * f(y[i], t, *args)\n", " i += 1\n", " t += delta_t\n", " \n", " return y" ] }, { "cell_type": "markdown", "id": "04ff3f37-e18c-4ca3-8581-2082b14eab22", "metadata": {}, "source": [ "## An example problem: reversible dimerization\n", "\n", "To have a concrete example problem, let us consider the dimerization of [hexokinase](https://en.wikipedia.org/wiki/Hexokinase). Hexokinases phosphorylate six-carbon sugars and are important metabolic enzymes. They exist in yeast cells in high concentration, being present in both monomeric and dimeric forms. The two forms bind glucose differently, so the relative concentrations of the monomeric and dimeric forms are of interest. Denoting A as a hexokinase monomer, the chemical reaction is $\\mathrm{A} + \\mathrm{A} \\rightleftharpoons AA$, with the forward reaction having rate constant $k_+$ and the reverse reaction having rate constant $k_-$. The dynamical equations for this system are\n", "\n", "\\begin{align}\n", "&\\frac{\\mathrm{d}c_\\mathrm{AA}}{\\mathrm{d}t} = k_+ c_\\mathrm{A}^2 - k_-\\,c_\\mathrm{AA},\\\\[1em]\n", "&\\frac{\\mathrm{d}c_\\mathrm{A}}{\\mathrm{d}t} = -2k_+ c_\\mathrm{A}^2 + 2k_-\\,c_\\mathrm{AA}.\n", "\\end{align}\n", "\n", "We can employ the conservation of mass relation\n", "\n", "\\begin{align}\n", "c_\\mathrm{A}^0 = c_\\mathrm{A} + 2c_\\mathrm{AA},\n", "\\end{align}\n", "\n", "where $c_\\mathrm{A}^0$ is the total concentration of hexokinase molecules, to reduce the dynamical system to a single equation,\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}c_\\mathrm{A}}{\\mathrm{d}t} = -2k_+\\,c_\\mathrm{A}^2 - k_-\\,c_\\mathrm{A} + k_-\\,c_\\mathrm{A}^0.\n", "\\end{align}\n", "\n", "To enable solving this using Euler's method, we need to code up the expression on the right hand side." ] }, { "cell_type": "code", "execution_count": 3, "id": "b83c5dd3-fc8c-4a7f-8b07-142cec4632b3", "metadata": {}, "outputs": [], "source": [ "def dimerization_rhs(cA, t, k_plus, k_minus, cA_total):\n", " \"\"\"\n", " Right hand side of dimerization ODE\n", " \"\"\"\n", " return -(k_minus + 2 * k_plus * cA) * cA + k_minus * cA_total" ] }, { "cell_type": "markdown", "id": "69068474-b470-4cbe-a77e-993b337adf4b", "metadata": {}, "source": [ "Note that I have explicitly put in time dependence in the function definition although $t$ does not appear in the expression. I do this because the Euler stepper we wrote above expects this, as does the automated integrator we will use later in this appendix.\n", "\n", "To solve, we need to specify parameters. We will use parameters obtained by [Hoggett and Kellett, 1992](https://dx.doi.org/10.1042%2Fbj2870567), which they obtained for the PI hexokinase in yeast in a solution containing 10 mM glucose. They determined that $k_+ = 0.25$ (µM·s)⁻¹ and $k_- = 3.1$ s⁻¹. In one of their experiments, they used $c_\\mathrm{A}^0 = 10$ µM." ] }, { "cell_type": "code", "execution_count": 4, "id": "3af75dad-277a-43af-bb51-025b80ee4dd4", "metadata": {}, "outputs": [], "source": [ "# Parameters\n", "k_plus = 0.25 # 1 / µM-s\n", "k_minus = 3.1 # 1 / s\n", "\n", "# Total concentration of hexokinase molecules\n", "cA_total = 10 # µM\n", "\n", "# Initial concentration of monomer (assume all monomeric)\n", "cA0 = 10 # µM\n", "\n", "# Total time we want to use\n", "t_max = 1 # s\n", "\n", "# Time step for integrator (50 ms)\n", "delta_t = 0.05 # s\n", "\n", "# Assemble parameters into args\n", "args = (k_plus, k_minus, cA_total)" ] }, { "cell_type": "markdown", "id": "b815bb1c-f1d3-4659-a1f7-87065fde17d6", "metadata": {}, "source": [ "Now we can solve using Euler's method!" ] }, { "cell_type": "code", "execution_count": 5, "id": "0fef3978-92e3-4740-8915-046772222d1d", "metadata": {}, "outputs": [], "source": [ "# Generate time points for plotting\n", "t_coarse = np.arange(int(t_max / delta_t) + 1) * delta_t\n", "\n", "# Solve for monomeric concentration\n", "cA = solve_euler(\n", " dimerization_rhs, np.array([cA0]), t_max, delta_t, args=(k_plus, k_minus, cA_total)\n", ")\n", "\n", "# Compute dimeric concentration using conservation of mass\n", "cAA = (cA_total - cA[:, 0]) / 2" ] }, { "cell_type": "markdown", "id": "85f9a19c-d4ee-468d-b2eb-c555de1ba612", "metadata": {}, "source": [ "Let's take a look at the plot of our solution." ] }, { "cell_type": "code", "execution_count": 6, "id": "9c7e01a4-33f9-4045-8bd7-fed7e8261400", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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(s)\",\n", " y_axis_label=\"concentration (µM)\",\n", " x_range=[0, 1],\n", ")\n", "p.line(t_coarse, cA[:, 0], line_width=2, legend_label=\"monomer\")\n", "p.line(t_coarse, cAA, color=\"orange\", line_width=2, legend_label=\"dimer\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "b5cce18e-700b-4c9f-97dc-1abdf35d3032", "metadata": {}, "source": [ "This seems to capture what we would expect, a decay of the monomer concentration with a corresponding increase in the dimer concentration.\n", "\n", "As is often the case when we are testing out numerical methods, it is good to compare to a known, analytical result. In this case, we can calculate the rather complicated analytical result. (We will not show the calculation here; only state the result.) Defining \n", "\n", "\\begin{align}\n", "\\zeta = \\frac{1}{\\sqrt{1 + 8 \\,\\frac{k_+}{k_-}\\,c_\\mathrm{A}^0}},\n", "\\end{align}\n", "\n", "the solution is\n", "\n", "\\begin{align}\n", "c_\\mathrm{A}(t) = \\frac{1}{4}\\frac{k_-}{k_+}\\left(\\zeta^{-1} \\tanh\\left[\\frac{k_- t}{2\\zeta} + \\mathrm{arctanh}\\left(\\zeta\\left(1 + 4\\, \\frac{k_+}{k_-}\\,c_\\mathrm{A,0}\\right)\\right)\\right] - 1\\right)\n", "\\end{align}\n", "\n", "if\n", "\\begin{align}\n", "\\zeta\\left(1+4\\,\\frac{k_+}{k_-}\\,c_\\mathrm{A,0}\\right) < 1\n", "\\end{align}\n", "\n", "and\n", "\n", "\\begin{align}\n", "c_\\mathrm{A}(t) = \\frac{1}{4}\\frac{k_-}{k_+}\\left(\\zeta^{-1} \\coth\\left[\\frac{k_- t}{2\\zeta} + \\mathrm{arccoth}\\left(\\zeta\\left(1 + 4\\, \\frac{k_+}{k_-}\\,c_\\mathrm{A,0}\\right)\\right)\\right] - 1\\right)\n", "\\end{align}\n", "\n", "if\n", "\n", "\\begin{align}\n", "\\zeta\\left(1+4\\,\\frac{k_+}{k_-}\\,c_\\mathrm{A,0}\\right) \\ge 1.\n", "\\end{align}\n", "\n", "We can code this up in Python, noting that Numpy does not have built-in coth and arccoth functions, so we have write those ourselves." ] }, { "cell_type": "code", "execution_count": 7, "id": "c4254418-f152-40d0-9a2b-c1cefd61b407", "metadata": {}, "outputs": [], "source": [ "def coth(x):\n", " \"\"\"Hyperbolic cotangent function.\"\"\"\n", " return 1 / np.tanh(x)\n", "\n", "\n", "def arccoth(x):\n", " \"\"\"Hyberbolic arccotangent function.\"\"\"\n", " return np.log((x + 1) / (x - 1)) / 2\n", "\n", "\n", "def cA_theor(t, k_plus, k_minus, cA_total, cA0):\n", " \"\"\"Analytical result for concentration of monomer over time\n", " for reversible dimerization.\"\"\"\n", " zeta = 1 / np.sqrt(1 + 8 * k_plus / k_minus * cA_total)\n", " arc_arg = zeta * (1 + 4 * k_plus / k_minus * cA0)\n", "\n", " # Which part of the solution we live on\n", " fun = np.tanh if arc_arg < 1 else coth\n", " arcfun = np.arctanh if arc_arg < 1 else arccoth\n", "\n", " prefactor = k_minus / k_plus / 4\n", " return prefactor * (fun(k_minus * t / 2 / zeta + arcfun(arc_arg)) / zeta - 1)" ] }, { "cell_type": "markdown", "id": "3c686bbc-d621-4496-a922-f0a13aba0c2a", "metadata": {}, "source": [ "Now we can compute correct values for $c_\\mathrm{A}$ and overlay them on the plot of the numerical result. 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dimerization_rhs, np.array([cA0]), t_max, delta_t, args=(k_plus, k_minus, cA_total)\n", ")\n", "\n", "# Compute dimeric concentration using conservation of mass\n", "cAA = (cA_total - cA[:, 0]) / 2\n", "\n", "# Generate new time points for plotting numerical solution\n", "t = np.arange(int(t_max / delta_t) + 1) * delta_t\n", "\n", "# Set up plot and populate with analytical solution\n", "p = bokeh.plotting.figure(\n", " frame_height=200,\n", " frame_width=300,\n", " x_axis_label=\"time (s)\",\n", " y_axis_label=\"concentration (µM)\",\n", " x_range=[0, 1],\n", ")\n", "\n", "# Populate plot and show\n", "p.line(t, cA[:, 0], line_width=2, legend_label=\"monomer\")\n", "p.line(t, cAA, color=\"orange\", line_width=2, legend_label=\"dimer\")\n", "p.circle(t_coarse, cA_analytical, fill_color=None)\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "694f0fb7-e453-4ab4-81da-e24c72c006ee", "metadata": {}, "source": [ "Much better!" ] }, { "cell_type": "markdown", "id": "3b17a8fd-9fea-4d07-8e24-cd2e7b21ac2a", "metadata": {}, "source": [ "## Variable step sizes can help speed the solution\n", "\n", "If we look at the above solution, we are still not quite hitting the analytical solution at short times, though we do well as the system approaches steady state. It makes sense, then, to take shorter time steps when the solution is changing rapidly and longer time steps when it is changing slowly. We would therefore employ a **variable step size algorithm**.\n", "\n", "Such an algorithm is employed in `scipy.optimize.odeint()`. It uses the Hindmarsh-Petzold algorithm, as implemented in LSODA as part of ODEPACK. (That word salad is mostly so you know what to enter into search engines to find more information about the algorithm.) We will discuss some other features of the algorithm momentarily.\n", "\n", "The interface for `scipy.integrate.odeint()` is the same as for the Euler integration function we just developed, except in place of `delta_t` and `t_max`, you specify for which time points you want the solution evaluated. Because `scipy.integrate.odeint()` does automatic variable time stepping, it chooses its *own* $\\Delta t$'s for each time step. It then interpolates its solutions to give you the values at the time points you ask for.\n", "\n", "Let's put this to use. We will use the same time points we used with Euler integration." ] }, { "cell_type": "code", "execution_count": 10, "id": "32ce98e3-f014-441e-9e2e-545315b6d7e0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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k_minus, cA_total)\n", ")\n", "\n", "# Add this one to the plot in red\n", "p.line(t, cA[:, 0], line_width=2, color=\"tomato\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "e7b18bb0-deb7-4c03-9759-40d09803348b", "metadata": {}, "source": [ "The `scipy.integrate.odeint()` function much more closely matches the analytical solution at all time points." ] }, { "cell_type": "markdown", "id": "39edec9c-4beb-49df-b5f7-4c456ea2ff6a", "metadata": {}, "source": [ "## Stiffness presents additional challenges\n", "\n", "Systems of ODEs that have a wide spread in time scales of dynamics are said to be **stiff**. Stiff ODEs offer challenges beyond the accuracy and time-stepping issues we have already explored with Euler's method. Stiff ODEs have different dynamical modes that occur at vastly different time scales. This usually arises from big differences in coefficients in the dynamical equations.\n", "\n", "We will consider a classic example of a stiff chemical reaction system proposed by H. H. Robertson, known as the Robertson problem. The chemical reactions and their rate constants are\n", "\n", "\\begin{align}\n", "&\\mathrm{Y} + \\mathrm{Z} \\longrightarrow \\mathrm{X};\\;\\;\\;k_1 = 10^4\\text{ M}^{-1}\\cdot\\text{s}^{-1}, \\\\[1em]\n", "&\\mathrm{X} \\longrightarrow \\mathrm{Y};\\;\\;\\;k_2 = 0.04\\text{ s}^{-1}, \\\\[1em]\n", "&\\mathrm{Y} + \\mathrm{Y} \\longrightarrow \\mathrm{Z};\\;\\;\\;k_3 = 3\\times10^7\\text{ M}^{-1}\\cdot\\text{s}^{-1}.\n", "\\end{align}\n", "\n", "Letting lowercase letters be the concentrations of the corresponding uppercase symbols, the dynamical equations are\n", "\n", "\\begin{align}\n", "&\\frac{\\mathrm{d}x}{\\mathrm{d}t} = k_1\\,y\\,z - k_2\\,x,\\\\[1em]\n", "&\\frac{\\mathrm{d}y}{\\mathrm{d}t} = -k_1\\,y\\,z + k_2\\,x - k_3\\,y^2,\\\\[1em]\n", "&\\frac{\\mathrm{d}z}{\\mathrm{d}t} = k_3\\,y^2.\n", "\\end{align}\n", "\n", "We see a huge range of rate constant values, ranging from $10^{-2}$ to $10^{7}$, a sign of stiffness. This is a nice system to study because we know two facts about it. First, an interesting feature of this system is that\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\frac{\\mathrm{d}y}{\\mathrm{d}t} + \\frac{\\mathrm{d}z}{\\mathrm{d}t} = 0,\n", "\\end{align}\n", "\n", "so that $x + y + z$ is always constant. Second, the steady state, the values of $x$, $y$, and $z$ for which all time derivatives vanish, is unique with $x = y = 0$, as given by setting $\\mathrm{d}z/\\mathrm{d}t = \\mathrm{d}x/\\mathrm{d}t = 0$. Because $x + y + z$ is constant, the steady state has $z$ equal to that constant. Knowing these facts will help us analyze correctness of numerical solutions.\n", "\n", "Let us now attempt to solve this problem with Euler's method, starting from an initial condition of $x = 1$ M and $y = z = 0$. With our initial condition, $x + y + z = 1$M for all time." ] }, { "cell_type": "code", "execution_count": 11, "id": "5176a888-9474-4c0f-8c1b-2d4f5a8ea4a9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/j_/c5r9ch0913v3h1w4bdwzm0lh0000gn/T/ipykernel_80041/1963278859.py:6: RuntimeWarning: overflow encountered in double_scalars\n", " dx_dt = k1 * y * z - k2 * x\n", "/var/folders/j_/c5r9ch0913v3h1w4bdwzm0lh0000gn/T/ipykernel_80041/1963278859.py:7: RuntimeWarning: overflow encountered in double_scalars\n", " dz_dt = k3 * y ** 2\n", "/var/folders/j_/c5r9ch0913v3h1w4bdwzm0lh0000gn/T/ipykernel_80041/1963278859.py:8: RuntimeWarning: invalid value encountered in double_scalars\n", " dy_dt = -dx_dt - dz_dt\n" ] } ], "source": [ "def robertson_rhs(xyz, t, k1, k2, k3):\n", " \"\"\"Right-hand-side of Robertson's stiff ODEs.\"\"\"\n", " # Unpack variables\n", " x, y, z = xyz\n", "\n", " dx_dt = k1 * y * z - k2 * x\n", " dz_dt = k3 * y ** 2\n", " dy_dt = -dx_dt - dz_dt\n", "\n", " return np.array([dx_dt, dy_dt, dz_dt])\n", "\n", "\n", "# Time steps\n", "delta_t = 0.001\n", "t_max = 10\n", "\n", "# Paramters\n", "k1 = 1e4\n", "k2 = 0.04\n", "k3 = 3e7\n", "\n", "# Initial condition\n", "xyz0 = np.array([1, 0, 0])\n", "xyz = solve_euler(robertson_rhs, xyz0, t_max, delta_t, args=(k1, k2, k3))" ] }, { "cell_type": "markdown", "id": "e5861a0c-fd24-4f7a-b072-992cfb8ed59b", "metadata": {}, "source": [ "We got a warning that we had overflow! This must mean the solver has made grievous errors, since we must always have $x + y + z = 1$. We can plot the solution to see what was going on. We will put $x$ in blue, $y$ in orange, and $z$ in red." ] }, { "cell_type": "code", "execution_count": 12, "id": "554aeb24-fdf6-43c1-8468-a22ea4d4e41b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1838" } }, "output_type": "display_data" } ], "source": [ "# Generate time points for plotting numerical solution\n", "t = np.arange(int(t_max / delta_t) + 1) * delta_t\n", "\n", "# Make plot\n", "p = bokeh.plotting.figure(\n", " frame_height=200,\n", " frame_width=300,\n", " x_axis_label=\"time (s)\",\n", " y_axis_label=\"conc (M)\",\n", " y_axis_type=\"log\",\n", " x_range=[0, 10],\n", " y_range=[1e-9, 1e2],\n", ")\n", "\n", "# Thin the points so the file of the plot is not so large\n", "p.line(t[::10], xyz[::10, 0], line_width=2)\n", "p.line(t[::10], xyz[::10, 1], line_width=2, color=\"orange\")\n", "p.line(t[::10], xyz[::10, 2], line_width=2, color=\"tomato\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "01c33e1d-3105-410e-b8be-ab82be7a2535", "metadata": {}, "source": [ "The concentration axis is on a log scale, so where the $y$ (orange) curve is missing, we are getting negative values. Importantly, looking right around 9.34 seconds, we see the solution explode. This is an example of **instability** that can plague explicit methods with stiff systems." ] }, { "cell_type": "markdown", "id": "cb59c338-acf5-4fa8-917d-f574fc1aeccc", "metadata": {}, "source": [ "## Implicit methods can handle stiffness, but are slower and harder to implement\n", "\n", "In contrast to explicit methods, implicit methods are much less susceptible to the types of catastrophic failures due to stiffness we see with explicit methods. Implicit methods employ a different kind of differencing formula. Recall that for Euler's method, we approximated the time derivative using the forward differencing as\n", "\n", "\\begin{align}\n", "\\frac{\\mathrm{d}y}{\\mathrm{d}t} \\approx \\frac{y(t+\\Delta t) - y(t)}{\\Delta t},\n", "\\end{align}\n", "\n", "where $y$ here is a generic solution to a system of ODEs, not to be confused with the concentration of species Y in the Robertson problem. This approximation of the derivative led to updating the solution at time $t + \\Delta t$ as\n", "\n", "\\begin{align}\n", "\\frac{y(t+\\Delta t) - y(t)}{\\Delta t} \\approx f(y(t), t).\n", "\\end{align}\n", "\n", "In the **backwards Euler** method, we instead use **backward differencing** to obtain a solution at time $t + \\Delta t$ as\n", "\n", "\\begin{align}\n", "\\frac{y(t+\\Delta t) - y(t)}{\\Delta t} \\approx f(y(t+\\Delta t), t+\\Delta t).\n", "\\end{align}\n", "\n", "Our solution is then updated according to\n", "\n", "\\begin{align}\n", "y(t+\\Delta t) = y(t) + \\Delta t f(y(t+\\Delta t), t+\\Delta t).\n", "\\end{align}\n", "\n", "This is now an *implicit* expression for $y(t+\\Delta t)$, since $y(t+\\Delta t)$ appears (in a possibly nonlinear way) on the right hand side. Because implicit methods require solving a set of nonlinear algebraic equations to update the solution, each step takes considerably more time to evaluate than for an explicit method. Also because of this requirement to solve algebraic systems at each time step, they are more difficult to implement. The (very big) upside is that they handle stiffness much better. (We will not go into details as to why and how they perform with respective to stiffness and stability, but that is a big, beautiful field of study in numerics.)\n", "\n", "The solution of the above algebraic equation for $y(t+\\Delta t)$ is a from of a **fixed point** problem of the form\n", "\n", "\\begin{align}\n", "x = g(x).\n", "\\end{align}\n", "\n", "The scipy.optimize module offered a function `scipy.optimize.fixed_point()` ([docs](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fixed_point.html)) to solve this problem. We can use this function to code up a backward Euler method." ] }, { "cell_type": "code", "execution_count": 13, "id": "215dcac0-07b7-4a7e-b08c-d740b89f0d0f", "metadata": {}, "outputs": [], "source": [ "def solve_backward_euler(f, y0, t_max, delta_t, args=()):\n", " \"\"\"Solve an ODE defined by y'(t) = f(y, t, *args)\n", " using backward Euler's method.\"\"\"\n", " # Initialize output array\n", " y = np.empty((int(t_max / delta_t) + 1, len(y0)))\n", "\n", " # Insert initial condition\n", " y[0] = y0\n", "\n", " # Start at t = 0, with index 0\n", " t = 0.0\n", " i = 0\n", "\n", " # Function to be used in fixed point iteration\n", " fp_func = lambda y, y_prev, t, delta_t, args: y_prev + delta_t * f(y, t, *args)\n", "\n", " # March forward in time\n", " while i < len(y) - 1:\n", " # Package args for fixed point function\n", " fp_args = (y[i], t, delta_t, args)\n", "\n", " # Solve for new y value and iterate\n", " y[i + 1] = scipy.optimize.fixed_point(fp_func, y[i], args=fp_args)\n", " i += 1\n", " t += delta_t\n", "\n", " return y" ] }, { "cell_type": "markdown", "id": "59ec2030-bcca-4dc8-89c7-9fc2df1d34e2", "metadata": {}, "source": [ "Now, let's try the same calculation as before with backward Euler." ] }, { "cell_type": "code", "execution_count": 14, "id": "d6b97d12-5edf-4963-a641-4b233d37951a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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vEZyBivP1fgUA3ANK8/3kXhIKhQrz/4Y69mgGyvP0mVqfBIiK8/VXeg0AGkrz+tKkcYq7+vP2GSM9lE268/2ZLeJM/2rz8DKFIGJQmwP3I14tDaFrA/OR+x+ogksD/3jUKMLzKwP0tDDI7OP7A/Vjd2CGZNsD/5tdoD9lqwP8V7hoh+aLA/otK4nv91sD8prqNOeYOwP7nHa6DrkLA/QboonFaesD/BHeVJuquwP4CinrEWubA/ESxG22vGsD/467/OudOwPxd845MA4bA/4fh7MkDusD85G0iyePuwPxpS+hqqCLE/+ts4dNQVsT/x353F9yKxP56GtxYUMLE/xxIIbyk9sT/H+QXWN0qxP7X7G1M/V7E/VTup7T9ksT/IVQGtOXGxPwR6bJgsfrE/DoAntxiLsT/+/2MQ/pexP8loSKvcpLE/0hbwjrSxsT88amvChb6xPxrdv0xQy7E/SxnoNBTYsT80DtSB0eSxP0UGaTqI8bE/PryBZTj+sT9GcO4J4gqyP878dC6FF7I/Q+vQ2SEksj+MiLMSuDCyP0/5w99HPbI/FE6fR9FJsj8nl9hQVFayP1v4+AHRYrI/ibx/YUdvsj/taOJ1t3uyP1rQjEUhiLI/Kibh1oSUsj8cETgw4qCyP+y94Fc5rbI/0/EgVIq5sj/JHDUr1cWyP6ZrUOMZ0rI/Gtqcgljesj9xRDsPkeqyPzJ5Q4/D9rI/mErECPACsz/Zn8OBFg+zP0qGPgA3G7M/XEIpilEnsz9vYG8lZjOzP3bF89d0P7M/hL+Qp31Lsz8iFhiagFezP4saU7V9Y7M/ubcC/3Rvsz9Xgt98ZnuzP3/ImTRSh7M/YaHZKziTsz/H/D5oGJ+zP2KyYe/yqrM/DJHRxse2sz/RbRb0lsKzP+kysHxgzrM/h+4WZiTasz964bq14uWzP8CNBHGb8bM/9sRUnU79sz+TtgRA/Ai0Pxj+ZV6kFLQ/FLHC/UYgtD8SbV0j5Cu0P1llcdR7N7Q/nXAyFg5DtD+HFs3tmk60Px2dZmAiWrQ/ExYdc6RltD/5awcrIXG0P05vNY2YfLQ/dOOvngqItD+Hi3hkd5O0Pxo3iuPenrQ/0c7YIEGqtD/pYFEhnrW0P5st2un1wLQ/Y7NSf0jMtD84u5Pmlde0P5xkbyTe4rQ/lTGxPSHutD+REh43X/m0PyJydBWYBLU/skBs3csPtT8XALeT+hq1P//O/zwkJrU/WXTr3UgxtT+bahh7aDy1P+zqHhmDR7U/OfiQvJhStT84avppqV21P0b44CW1aLU/OUTE9LtztT8X5R3bvX61P7JxYd26ibU/MYv8/7KUtT+F51ZHpp+1P7pb0reUqrU/SebKVX61tT88uZYlY8C1P1FEhitDy7U/7T7kax7WtT8fsvXq9OC1P2UC+qzG67U/e/kqtpP2tT8I0LwKXAG2PzU33q4fDLY/OmK4pt4Wtj/FD2/2mCG2P2GTIKJOLLY/ut7lrf82tj/ZitIdrEG2P0Ph9PVTTLY/DOVVOvdWtj/OW/nulWG2P5jW3RcwbLY/x7r8uMV2tj/HSkrWVoG2P8OutXPji7Y/T/0olWuWtj/wQ4k+76C2P5WPtnNuq7Y/CvWLOOm1tj9Qmd+QX8C2P+G5goDRyrY/6bRBCz/Vtj90EeQ0qN+2P3iHLAEN6rY/4QfZc230tj+IxKKQyf62Pw84PlshCbc/vy1b13QTtz89yaQIxB23P1aOwfIOKLc/imhTmVUytz+1svf/lzy3P4s+RyrWRrc/DlzWGxBRtz/74DTYRVu3Pxww7mJ3Zbc/mECJv6Rvtz8qpYjxzXm3P0yTavzyg7c/WOqo4xOOtz+ZOrmqMJi3P0TMDFVJorc/d6YQ5l2stz8Xli1hbra3P6g0yMl6wLc/He9AI4PKtz+ODPRwh9S3P+q0ObaH3rc/mfdl9oPotz8R0sg0fPK3P102rnRw/Lc/mhFeuWAGuD9kUhwGTRC4PzPvKF41Grg/uey/xBkkuD8lZBk9+i24P12JacrWN7g/M7Hgb69BuD+IV6swhEu4P18l8g9VVbg/7/bZECJfuD+f4YM262i4P/45DYSwcrg/qJmP/HF8uD8q5SCjL4a4P81R03rpj7g/YGu1hp+ZuD/0GdLJUaO4P42nMEcArbg/x8XUAau2uD9uk778UcC4PxSi6jr1ybg/lPtRv5TTuD+KJ+qMMN24P8cwpabI5rg/tapxD13wuD+1tjrK7fm4P2sJ6Nl6A7k/DfBdQQQNuT+bVX0Diha5PxbIIyMMILk/pn0ro4opuT+5WWuGBTO5Px/yts98PLk/E5TegfBFuT88Sa+fYE+5P6nc8ivNWLk/w99vKTZiuT8xr+mam2u5P7N3IIP9dLk//zrR5Ft+uT+H1LXCtoe5Pzz+hB8Okbk/R1Xy/WGauT+/Xq5gsqO5P0mMZkr/rLk/xUDFvUi2uT/V1HG9jr+5P3ibEEzRyLk/iOZCbBDSuT87C6cgTNu5P59m2GuE5Lk//WFvULntuT9DdwHR6va5P2E1IfAYALo/n0ResEMJuj/oakUUaxK6PxCQYB6PG7o/FsI20a8kuj9SOUwvzS26P6hcIjvnNro/r8U39/0/uj/ORAhmEUm6P1XlDIohUro/i/G7ZS5buj+79oj7N2S6Py7J5E0+bbo/Log9X0F2uj/xof4xQX+6P5DXkMg9iLo/3kBaJTeRuj9QUL5KLZq6P9LWHTsgo7o/lwfX+A+suj/de0WG/LS6P7Y2wuXlvbo/xKijGczGuj/osz0kr8+6P/yu4QeP2Lo/a2nexmvhuj/hLoBjReq6P97KEOAb87o/UYzXPu/7uj8fSRmCvwS7P7JhGKyMDbs/dMQUv1YWuz9S8Uu9HR+7Py39+KjhJ7s/TZVUhKIwuz/FApVRYDm7P90t7hIbQrs/aaGRytJKuz8sjq56h1O7PxnOcSU5XLs/sOcFzedkuz84EZNzk227Pwk0Pxs8drs/wO8txuF+uz93nYB2hIe7P/dSVi4kkLs/4OXL78CYuz/P7vu8WqG7P3zM/pfxqbs/1abqgoWyuz8UctN/Fru7P8zxypCkw7s/+Lvgty/Muz/8OyL3t9S7P6S1mlA93bs/IkhTxr/luz//8FJaP+67PxOPng689rs/a+U45TX/uz8xniLgrAe8P45NWgEhELw/g3TcSpIYvD/Kg6O+ACG8P6Hep15sKbw/nN3fLNUxvD9t0T8rOzq8P6oFulueQrw/jMM+wP5KvD+uVLxaXFO8P8AFHy23W7w/PClROQ9kvD8TGjuBZGy8P1U+wwa3dLw/3AnOywZ9vD/lAD7SU4W8P6+68xuejbw/F+TNquWVvD8lQqmAKp68P6K0YJ9sprw/nTjNCKyuvD/z6sW+6La8P9YKIMMiv7w/SPyuF1rHvD+USkS+js+8P8uqr7jA17w/K/6+CPDfvD+XVD6wHOi8PwLv97BG8Lw/y0G0DG74vD8n9znFkgC9P4TxTdy0CL0/0k2zU9QQvT/wZSst8Ri9P/DSdWoLIb0/bG9QDSMpvT/MWXcXODG9P5X2pIpKOb0/qfKRaFpBvT+DRfWyZ0m9P38zhGtyUb0/B1Dyk3pZvT/Pf/EtgGG9Pwb7MTuDab0/g09ivYNxvT/uYi+2gXm9P+50RCd9gb0/RCFLEnaJvT/yYet4bJG9P1mRy1xgmb0/SWyQv1GhvT8iFN2iQKm9P+AQUwgtsb0/MVOS8Ra5vT97Njlg/sC9P+WC5FXjyL0/Y28v1MXQvT+1o7Pcpdi9P2Q6CXGD4L0/w8LGkl7ovT/mQoFDN/C9P5Q5zIQN+L0/Q6A5WOH/vT//7Fm/sge+P1wUvLuBD74/WIvtTk4Xvj9NSXp6GB++P9XJ7D/gJr4/nw7OoKUuvj9ToaWeaDa+P3GV+TopPr4/JopOd+dFvj8arCdVo02+P0y3BtZcVb4/4fhr+xNdvj/oUNbGyGS+Py80wzl7bL4/Ba6uVSt0vj/4YRMc2Xu+P6ONao6Eg74/Zwosri2Lvj8gT8581JK+P+1xxvt4mr4/3CmILBuivj+h0IUQu6m+P0xkMKlYsb4/7Ij39/O4vj9Nikn+jMC+P49dk70jyL4/3qJAN7jPvj8Rp7tsSte+P0NlbV/a3r4/gYi9EGjmvj9bbRKC8+2+P4sj0bR89b4/gm9dqgP9vj8FzBlkiAS/P8FrZ+MKDL8/1jqmKYsTvz9u4DQ4CRu/P0LAcBCFIr8/J/y1s/4pvz+XdV8jdjG/PzTPxmDrOL8/VG5EbV5Avz9yfC9Kz0e/P7ro3fg9T78/gmmkeqpWvz++fdbQFF6/P4Buxvx8Zb8/cFDF/+Jsvz8yBSPbRnS/P+U8LpCoe78/jXc0IAiDvz9+BoKMZYq/P84NYtbAkb8/t4Ue/xmZvz8CPAAIcaC/P2rVTvLFp78/+s5Qvxivvz95f0twaba/P8AYgwa4vb8/Gqk6gwTFvz+cHLTnTsy/P4A+MDWX078/e7rubN3avz8SHi6QIeK/P+nZK6Bj6b8/HEMknqPwvz+GlFKL4fe/PxHw8Ggd/78/AjAcnCsDwD8ibDB9xwbAP9GbUFhiCsA/kKQXLvwNwD+Z4h//lBHAP4IpA8wsFcA/2cRalcMYwD/HeL9bWRzAP6+CyR/uH8A/xJkQ4oEjwD+x7yujFCfAPygxsmOmKsA/hoY5JDcuwD9mlFflxjHAPz58oadVNcA/+tyra+M4wD+M0woycDzAP4T7Ufv7P8A/qW8UyIZDwD+QyuSYEEfAPyQnVW6ZSsA/QiH3SCFOwD9R1lspqFHAP8XlExAuVcA/tnGv/bJYwD90H77yNlzAPxQYz++5X8A/9Qhx9TtjwD9cJDIEvWbAP/choBw9asA/cD9IP7xtwD/qQLdsOnHAP5xxeaW3dMA/UKQa6jN4wD/tMyY7r3vAPwcEJ5kpf8A/WoGnBKOCwD9cojF+G4bAP7jnTgaTicA/3lyInQmNwD9/mGZEf5DAPw+9cfvzk8A/Vnkxw2eXwD/kCC2c2prAP5M064ZMnsA/EFPyg72hwD9RSciTLaXAPyaL8racqMA/ohv27QqswD+ljVc5eK/AP1gEm5nkssA/pTNED1C2wD+7YNaaurnAP4Ri1DwkvcA/I6LA9YzAwD9mGx3G9MPAP0Zda65bx8A/YIosr8HKwD9sWeHIJs7AP7MVCvyK0cA/hp8mSe7UwD+3bLawUNjAPwWJODOy28A/oZYr0RLfwD+Vzg2LcuLAPzwBXWHR5cA/sZaWVC/pwD9KjzdljOzAPwSEvJPo78A/9Kah4EPzwD+2w2JMnvbAP+M/e9f3+cA/fBtmglD9wD9a8Z1NqADBP5b3nDn/A8E/BQDdRlUHwT+XeNd1qgrBP8prBcf+DcE/FIHfOlIRwT9R/d3RpBTBPyrDeIz2F8E/glMna0cbwT/czWBulx7BP8nwm5bmIcE/TRpP5DQlwT9KSPBXgijBP+MY9fHOK8E/5srSshovwT80Pv6aZTLBPyL066qvNcE/4w8Q4/g4wT/sVt5DQTzBP1Mxys2IP8E/OqpGgc9CwT8rcMZeFUbBP4fVu2ZaScE/19CYmZ5MwT87/c734U/BP8iaz4EkU8E/5I4LOGZWwT+sZPMap1nBP09N9yrnXME/ciCHaCZgwT+PXBLUZGPBP0snCG6iZsE/2k3XNt9pwT9fRe4uG23BP0Iru1ZWcME/ksWrrpBzwT9bgy03ynbBPw99rfACesE/yXSY2zp9wT/B1lr4cYDBP5G5YEeog8E/n94Vyd2GwT9psuV9EorBP+hMO2ZGjcE/43GBgnmQwT9GkSLTq5PBP37HiFjdlsE/yd0dEw6awT+OSksDPp3BP70xeiltoME/FGUThpujwT+CZH8ZyabBP3heJuT1qcE/NTBw5iGtwT8pZsQgTbDBPzc8ipN3s8E/Fp4oP6G2wT+jJwYkyrnBPyQliULyvME/qpMXmxnAwT9eIRcuQMPBP9Et7ftlxsE/S8r+BIvJwT8curBJr8zBP+1yZ8rSz8E/EB2Hh/XSwT/Mk3OBF9bBP69lkLg42cE/0tRALVncwT9A1+ffeN/BPyMX6NCX4sE/JvOjALblwT/Bfn1v0+jBP3yC1h3w68E/PXwQDAzvwT+bn4w6J/LBPyPWq6lB9cE/or/OWVv4wT91slVLdPvBP8y7oH6M/sE/+Z8P9KMBwj+62gGsugTCP3mf1qbQB8I/oNns5OUKwj/dLKNm+g3CP2j1VywOEcI/SUhpNiEUwj+p8zSFMxfCPwt/GBlFGsI/nStx8lUdwj959JsRZiDCP/KO9XZ1I8I/zWraIoQmwj+VsqYVkinCP9FLtk+fLMI/Utdk0asvwj92sQ2btzLCP2nyC63CNcI/bm66B804wj8atnOr1jvCP58WkpjfPsI/C5pvz+dBwj+GB2ZQ70TCP53jzhv2R8I/e3ADMvxKwj8urlyTAU7CP+1aM0AGUcI/UvPfOApUwj+Vsrp9DVfCP9ySGw8QWsI/bU1a7RFdwj/0Ws4YE2DCP8LzzpETY8I/CBCzWBNmwj8XaNFtEmnCP6J0gNEQbMI/+24WhA5vwj9IUemFC3LCP8/WTtcHdcI/JXyceAN4wj9yfydq/nrCP7LgRKz4fcI/5WFJP/KAwj9Xh4kj64PCP9WXWVnjhsI/6JwN4dqJwj8XY/m60YzCPxR6cOfHj8I/CDXGZr2Swj/Bqk05spXCP/G1WV+mmMI/Z/U82Zmbwj9FzEmnjJ7CPz9i0sl+ocI/zKMoQXCkwj9sQp4NYafCP9O0hC9RqsI/JTctp0Ctwj80y+h0L7DCP7M4CJkds8I/ZQ3cEwu2wj9lnbTl97jCP1AD4g7ku8I/gyC0j8++wj9MnXpousHCPyHphJmkxMI/3DoiI47Hwj/mkKEFd8rCP3SxUUFfzcI/wCqB1kbQwj8tU37FLdPCP45Jlw4U1sI/VvUZsvnYwj/EBlSw3tvCPxz3kgnD3sI/3ggkvqbhwj/2R1TOieTCP+6JcDps58I/I27FAk7qwj/3XZ8nL+3CPweNSqkP8MI/VvkSiO/ywj+Ea0TEzvXCPwR3Kl6t+MI/QXoQVov7wj/cnkGsaP7CP9bZCGFFAcM/wuuwdCEEwz/8YITn/AbDP8+RzbnXCcM/q6LW67EMwz9YhOl9iw/DPyH0T3BkEsM/AHxTwzwVwz/ccj13FBjDP6j8VozrGsM/mArpAsIdwz9XWzzblyDDPyh7mRVtI8M/IsRIskEmwz9SXpKxFSnDP+4/vhPpK8M/ii0U2bsuwz82utsBjjHDP7tHXI5fNMM/wAbdfjA3wz/09qTTADrDP0Pn+ozQPMM/+3Ulq58/wz8DEWsubkLDP/n1ERc8RcM/ZjJgZQlIwz/ro5sZ1krDP2b4CTSiTcM/J67wtG1Qwz8TFJWcOFPDP9BJPOsCVsM/8j8rocxYwz8ouKa+lVvDP2ZF80NeXsM/BkxVMSZhwz/4ARGH7WPDP/RuakW0ZsM/l2ylbHppwz+RpgX9P2zDP9aazvYEb8M/uZlDWslxwz8jxqcnjXTDP6wVPl9Qd8M/1VBJARN6wz8jEwwO1XzDP1DLyIWWf8M/a7vBaFeCwz8K+Ti3F4XDP2dtcHHXh8M/j9Wpl5aKwz+HwiYqVY3DP3OZKCkTkMM/vJPwlNCSwz86v79tjZXDP1X+1rNJmMM/Ngh3ZwWbwz/daOCIwJ3DP1uBUxh7oMM/6ocQFjWjwz8WiFeC7qXDP+FiaF2nqMM/8s6Cp1+rwz+uWOZgF67DP2Ri0onOsMM/cCSGIoWzwz9irUArO7bDPyTiQKTwuMM/F37FjaW7wz9AEw3oWb7DP2YKVrMNwcM/OqPe78DDwz9+9OSdc8bDPx7spr0lycM/Xk9iT9fLwz/6ulRTiM7DP0qju8k40cM/Y1TUsujTwz858tsOmNbDP8l4D95G2cM/ObyrIPXbwz/waO3Wot7DP84DEQFQ4cM/N+pSn/zjwz9DUu+xqObDP+JKIjlU6cM/8bsnNf/rwz9rZjumqe7DP33kmIxT8cM/s6l76Pzzwz8PAx+6pfbDPzQXvgFO+cM/fuaTv/X7wz8uS9vznP7DP3z5zp5DAcQ/w3+pwOkDxD+kRqVZjwbEPxaR/Gk0CcQ/mnzp8dgLxD9KAabxfA7EPwvya2kgEcQ/mvx0WcMTxD+1qfrBZRbEP0RdNqMHGcQ/YFZh/agbxD+Kr7TQSR7EP8BeaR3qIMQ/nTW444kjxD9z4dkjKSbEP3jrBt7HKMQ/0rh3EmYrxD/IimTBAy7EP9F+BeugMMQ/uo6Sjz0zxD/GkEOv2TXEP8E3UEp1OMQ/LhPwYBA7xD9cj1rzqj3EP4D1xgFFQMQ/3WtsjN5CxD/V9YGTd0XEPxF0PhcQSMQ/mKTYF6hKxD/tIoeVP03EPw==\"},\"shape\":[1001],\"dtype\":\"float64\",\"order\":\"little\"}]]}}},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p2194\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p2195\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2190\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"tomato\",\"line_width\":2}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2191\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"tomato\",\"line_alpha\":0.1,\"line_width\":2}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2192\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"line_color\":\"tomato\",\"line_alpha\":0.2,\"line_width\":2}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p2126\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p2154\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p2155\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p2156\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p2157\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p2158\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p2159\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p2160\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LogAxis\",\"id\":\"p2147\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"LogTicker\",\"id\":\"p2148\",\"attributes\":{\"num_minor_ticks\":10,\"mantissas\":[1,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"LogTickFormatter\",\"id\":\"p2150\"},\"axis_label\":\"conc 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root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p2123" } }, "output_type": "display_data" } ], "source": [ "# Solve using backward Euler\n", "xyz = solve_backward_euler(robertson_rhs, xyz0, t_max, delta_t, args=(k1, k2, k3))\n", "\n", "# Make same plot as we did with explicit method\n", "p = bokeh.plotting.figure(\n", " frame_height=200,\n", " frame_width=300,\n", " x_axis_label=\"time (s)\",\n", " y_axis_label=\"conc (M)\",\n", " y_axis_type=\"log\",\n", " x_range=[0, 10],\n", " y_range=[1e-9, 1e2],\n", ")\n", "p.line(t[::10], xyz[::10, 0], line_width=2)\n", "p.line(t[::10], xyz[::10, 1], line_width=2, color=\"orange\")\n", "p.line(t[::10], xyz[::10, 2], line_width=2, color=\"tomato\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "fb22b46f-a678-4a18-acf9-7f60a2040ce0", "metadata": {}, "source": [ "The numerical stability issues are gone. The cost, though, is that the calculation takes much longer per step. We only integrated for 10 seconds, but the level of $z$ is still very far from its steady state value, so we have a lot more integrating to do! Our implementation of backward Euler would take too long to integrate." ] }, { "cell_type": "markdown", "id": "aeee337c-5f89-4302-8fb9-d51d1befd78b", "metadata": {}, "source": [ "## The Hindmarsh-Petzold algorithm is the best of both worlds\n", "\n", "As we have seen some of the challenges of numerically solving systems of ODEs, we desire and ODE solver that can:\n", "\n", "1. Take small steps when the dynamics are changing rapidly and large steps when they are not.\n", "2. Use explicit time stepping when stiffness is not an issue (for speed), and implicit when it is (for stability).\n", "\n", "The Hindmarsh-Petzold algorithm does this. It uses variable time stepping and also detects stiffness and switches to implicit time stepping when necessary.\n", "\n", "Importantly, in the Robertson system, we want to take tiiiiiny time steps at the beginning to accurately capture fast transients. These are missing in our naive Euler and backwards Euler time stepping, but `scipy.integrate.odeint()` captures them. Also because of the variable time stepping and speed, we can run the solver for much much longer, capturing the dynamics all the way up to the steady state. This is really powerful, as it is quite often the case that the dynamics of chemical reaction systems vary across many time scales." ] }, { "cell_type": "code", "execution_count": 15, "id": "3435a730-40c8-47d9-be53-d78e2b726ff1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\"},\"shape\":[4000],\"dtype\":\"float64\",\"order\":\"little\"}],[\"y\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"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" const render_items = [{\"docid\":\"ef4fb938-18a8-4f83-85c1-ed8f9671da9c\",\"roots\":{\"p2432\":\"4bb852d6-733d-4718-b573-075b51c3ddde\"},\"root_ids\":[\"p2432\"]}];\n", " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p2432" } }, "output_type": "display_data" } ], "source": [ "# Time points we want, on a log scale\n", "t = np.logspace(-5, 7, 4000)\n", "\n", "# Integrate ODES\n", "xyz = scipy.integrate.odeint(robertson_rhs, xyz0, t, args=(k1, k2, k3))\n", "\n", "p = bokeh.plotting.figure(\n", " frame_height=200,\n", " frame_width=300,\n", " x_axis_label=\"time\",\n", " y_axis_label=\"conc\",\n", " x_axis_type=\"log\",\n", " y_axis_type=\"log\",\n", " y_range=[1e-9, 1e2],\n", " x_range=[1e-5, 1e7],\n", ")\n", "p.line(t, xyz[:, 0], line_width=2)\n", "p.line(t, xyz[:, 1], line_width=2, color=\"orange\")\n", "p.line(t, xyz[:, 2], line_width=2, color=\"tomato\")\n", "\n", "bokeh.io.show(p)" ] }, { "cell_type": "markdown", "id": "9bf7763c-daed-4f3b-85ad-91f2bfe2798c", "metadata": {}, "source": [ "This is great! We capture the short timescale rise of $y$ (the orange curve) on the scale of tens or milliseconds, and we still see the approach to steady state, which happens on the scale of $10^5$ seconds, or about one day.\n", "\n", "The small kink in the $z$-curve (the red one) is from when the solver shifted between explicit to implicit. The error therein is small, though, less than one part per million of the steady state level.\n", "\n", "So, going forward, `scipy.integrate.odeint()` is a very powerful tool for numerically solving chemical systems. For situations where it has troubles, you would need to dig much deeper into the structure of the problem to choose or develop the appropriate numerical methods." ] }, { "cell_type": "markdown", "id": "3751ca64-3583-40db-a318-9c17720e7278", "metadata": { "tags": [] }, "source": [ "## Afterthought: A note about the solving the backward difference equation\n", "\n", "Generally, the methods for solving $y(t+\\Delta t) = y(t) + \\Delta t f(y(t+\\Delta t), t+\\Delta t)$ involve techniques in numerical optimization, classically including fixed point iterations, but for illustrative purposes, I show how to solve for time steps with backward Euler for the Robertson system.\n", "\n", "For ease of notation, temporarily let $x = x(t+\\Delta t)$, $y = y(t+\\Delta t)$, $z = z(t+\\Delta t)$, and $x_0 = x(t)$, $y_0 = y(t)$, $z_0 = z(t)$. Then, to update the solution from $(x_0, y_0, z_0)$ tp $(x, y, z)$, we have to solve\n", "\n", "\\begin{align}\n", "&x = x_0 + \\Delta t (k_1 yz - k_2 x),\\\\[1em]\n", "&y = y_0 + \\Delta t(-k_1 yz + k_2 x - k_3 y^2),\\\\[1em]\n", "&z = z_0 + \\Delta t k_3 y^2.\n", "\\end{align}\n", "\n", "Inserting the expression for $z$ into that for $x$ yields\n", "\n", "\\begin{align}\n", "x = x_0 + \\Delta t(k_1 y(z_0 + \\Delta t k_3 y^2) - k_2 x).\n", "\\end{align}\n", "\n", "This can be rearranged to give $x$ as a function of $y$.\n", "\n", "\\begin{align}\n", "x = \\frac{1}{1 + \\Delta t k_2}\\left(x_0 + \\Delta t k_1 y(z_0 + \\Delta t k_3 y^2)\\right)\n", "\\end{align}\n", "\n", "Inserting this expressions we have derived for $x$ and $z$ as functions only of $y$ into our expression for $y$ yields\n", "\n", "\\begin{align}\n", "y = y_0 + \\Delta t\\left(-k_1 y(z_0 + \\Delta t k_3 y^2) + \\frac{k_2}{1 + \\Delta t k_2}\\left(x_0 + \\Delta t k_1 y(z_0 + \\Delta t k_3 y^2)\\right) - k_3 y^2\\right).\n", "\\end{align}\n", "\n", "This is a cubic polynomial in $y$ that can be rearranged to give\n", "\n", "\\begin{align}\n", "\\Delta t^2\\,k_1\\,k_3\\left(1 - \\frac{\\Delta t k_2}{1 + \\Delta t k_2}\\right)y^3 + \\Delta t k_3 y^2 + \\left(1 + \\Delta t k_1 z_0\\left(1 - \\frac{\\Delta t k_2}{1 + \\Delta t k_2}\\right)\\right)y - y_0 -\\frac{\\Delta t k_2}{1 + \\Delta t k_2}\\,x_0 = 0.\n", "\\end{align}\n", "\n", "By the Decartes Rule of Signs, this cubic has a single positive real root, which we can find for $y$, and then determine $z$ and $y$ by substitution of the solution for $y$. This is implemented below." ] }, { "cell_type": "code", "execution_count": 16, "id": "d2b594bf-23de-40c0-be76-a3568851471c", "metadata": {}, "outputs": [], "source": [ "def solve_timestep_robertson(xyz0, delta_t, k1, k2, k3):\n", " \"\"\"Solves for the implicit time step for use in backward\n", " Euler for the Robertson problem.\"\"\"\n", " # Unpack previous time step\n", " x0, y0, z0 = xyz0\n", " \n", " # Compute coefficients of cubic\n", " k2_ratio_term = delta_t * k2 / (1 + delta_t * k2)\n", " a = delta_t**2 * k1 * k2 * (1 - k2_ratio_term)\n", " b = delta_t * k3\n", " c = 1 + delta_t * k1 * z0 * (1 - k2_ratio_term)\n", " d = -y0 - k2_ratio_term * x0\n", " \n", " # Solve polynomial\n", " roots = np.roots([a, b, c, d])\n", "\n", " # y is the positive real root\n", " y = roots[np.logical_and(np.isreal(roots), roots > 0)][0]\n", " \n", " # Compute x and z\n", " z = z0 + delta_t * k3 * y**2\n", " x = (x0 + delta_t * k1 * y * z) / (1 + delta_t * k2)\n", " \n", " return np.array([x, y, z])" ] }, { "cell_type": "markdown", "id": "04693a42-80b7-4eb6-b727-345d547ff2c3", "metadata": {}, "source": [ "It is not necessary to use this, since fixed point iteration works fine." ] }, { "cell_type": "markdown", "id": "40ac3bae-8cb2-494a-ad78-1ea52032b418", "metadata": {}, "source": [ "
\n", "\n", "## References\n", "\n", "- Hoggett, J. G. and Kellett, G. L., Kinetics of the monomer-dimer reaction of yeast hexokinase PI, _Biochem. J._, 287, 567–572, 1992. ([link](https://doi.org/10.1042/bj2870567))\n", "- Robertson, H. H., The soluton of a set of reaction rate equations, In _Numerical Analysis: An Introduction_, Walsh, J., Ed., Academic Press, 178–182, 1967." ] }, { "cell_type": "markdown", "id": "d4f002e2-e8e9-4fce-9c0f-d0987304b30f", "metadata": {}, "source": [ "## Computing environment" ] }, { "cell_type": "code", "execution_count": 17, "id": "3baec66d-9af1-4d7e-8fa4-21f731193ece", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python implementation: CPython\n", "Python version : 3.10.10\n", "IPython version : 8.10.0\n", "\n", "numpy : 1.23.5\n", "scipy : 1.10.0\n", "bokeh : 3.1.0\n", "jupyterlab: 3.5.3\n", "\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -v -p numpy,scipy,bokeh,jupyterlab" ] } ], "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": "3.10.10" } }, "nbformat": 4, "nbformat_minor": 5 }