{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"\n",
"\n",
"Sensitivity analysis and optimization with dolfin-adjoint
\n",
"
\n",
"
\n",
"\n",
"
\n",
"Simon Funke
\n",
"Slides: https://goo.gl/W8J51i
\n",
"
\n",
"13th October 2016, UNISA Symposium\n",
"
\n",
"
\n",
"Contributors: Patrick Farrell, Marie Rognes\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Sensitivity analysis\n",
"\n",
"\n",
"**Given:** \n",
"\n",
"* A PDE with some parameter(s).\n",
"\n",
"* A (scalar) output derived from the solution."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"**Goal:**\n",
"\n",
"* Compute the sensitivity of the outout with respect to the parameters."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Why adjoints are useful\n",
"\n",
"The solution of the adjoint PDE allows us to evaluate the sensitivity with **arbitrary** parameters"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"-- at a **fixed cost**!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## In maths\n",
"\n",
"**Given:** \n",
"\n",
"* PDE $F(u; m) = 0$ with solution $u$ and parameter $m$.\n",
"\n",
"* A functional $J(u, m)$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"**What the adjoint approach gives us:**\n",
"\n",
"* Efficiently compute $\\frac{\\text{d}J}{\\text{dm}}$ for any $m$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## What is an adjoint \n",
"\n",
"Given a PDE and a functional, the adjoint is \n",
"\n",
"* a linear PDE derived from the original (\"forward) system.\n",
"* which depends on the forward solution u and the functional J,\n",
"* that in general is quite hard to derive\n",
"* and is useful for lots of things in computational science."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Adjoints are used in many applications\n",
"\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## The problem\n",
"\n",
"*[T]he automatic generation of optimal (in terms of robustness and efficiency) adjoint versions of large-scale simulation code is one of the great open challenges in the field of High-Performance Scientific Computing.*\n",
"\n",
"\"The Art of Differentiating Computer Programs\", Naumann (2011)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"*Considering the importance of design to .. all of engineering, it is\n",
"perhaps surprising that the development of adjoint codes has not\n",
"been more rapid .. [I]t seems likely that part of the reason is its\n",
"complexity.*\n",
"\n",
"\"An Introduction to the Adjoint Approach to Design\" (Giles and Pierce, 2000)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## The traditional way of computing adjoints\n",
"\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"### Fundamental idea\n",
"\n",
"A model is a sequence of elementary instructions. Differentiate each in turn, and\n",
"compose with the chain rule."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## The dolfin-adjoint approach\n",
"\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"### Fundamental idea\n",
"A model is a sequence of equation solves. Differentiate each in turn, and\n",
"compose with the chain rule. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# dolfin-adjoint automates adjoints and PDE-constrained optimization*\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"*for FEniCS models"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## dolfin-adjoint annotates the symbolic equation of the PDE constraint\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## dolfin-adjoint automatically derives the symbolic adjoint equations\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## dolfin-adjoint solves forward/adjoint problems until the optimal solution is found\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Advantages of the dolfin-adjoint approach\n",
"\n",
"* The adjoint derivation is **totally automatic** (∼3–10 lines)\n",
"* The adjoint is **very efficient** (examples later)\n",
"* The adjoint can automatically use **checkpointing**\n",
"* The adjoint works **naturally in parallel** (both MPI and OpenMP)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Why does it run in parallel?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## The FEniCS pipeline is employed both for the forward and the adjoint problem \n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Live demo"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Imagine with given have a FEniCS solver\n",
"\n",
"It does not really matter which one. For example a heat-equation solver:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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zB0t72Ay+x4id2QBgsdK3IWJnNtVuTVFn0ip8x8GKeuZo4pov23AOyxIXfGJ9pbJ2MlJX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\nDPJVOgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from dolfin import *\n",
"from dolfin_adjoint import *\n",
"#adj_reset()\n",
"\n",
"mesh = UnitSquareMesh(40, 40)\n",
"V = FunctionSpace(mesh, \"CG\", 2)\n",
"\n",
"v = TestFunction(V)# Testfunction \n",
"u_ = Function(V) # Old u\n",
"u = Function(V) # New u\n",
"f = Function(V) # Forcing term\n",
"f.vector()[:] = 1\n",
"nu = Function(V) # Viscosity\n",
"nu.vector()[:] = 0.001\n",
"\n",
"t = 0.0\n",
"end = 20\n",
"timestep = Constant(1)\n",
"\n",
"# Variational form\n",
"F = (u - u_)/timestep*v*dx + nu*inner(grad(u), grad(v))*dx - f*v*dx\n",
"bc = DirichletBC(V, 0.0, \"on_boundary\")\n",
"\n",
"# Time loop\n",
"while (t <= end):\n",
" solve(F == 0, u, bc)\n",
" u_.assign(u)\n",
" t += float(timestep)\n",
"plot(u)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## In order to use dolfin-adjoint, we need to make change one line\n",
"\n",
"On the second line:\n",
"```python\n",
"from dolfin_adjoint import *\n",
"```\n",
"With that change, dolfin-adjoint will record all equations that are being solved."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Now we can compute the define the functional. Let's say we are interested in:\n",
"\n",
"$J = \\frac{1}{2}\\int_\\Omega u(T) \\cdot u(T) \\textrm{d}x +\\frac{1}{2}\\int_\\Omega f^2 \\textrm{d}x$ "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"In code:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"J = Functional(u*u*dx*dt[FINISH_TIME] + f**2*dx*dt[START_TIME])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Now we can compute sensitivities\n",
"\n",
"For example with respect to $f$:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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KZXbly86vDIAqoLFrpGBEoLEJV6nrzn38RmWfNYBX4QYaFbezCaHHm8sEXp9Zf3T/1A2N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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ctrl = Control(f)\n",
"\n",
"dJdf = compute_gradient(J, ctrl, forget=False, project=True)\n",
"plot(dJdf)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## or with respect to more parameters\n",
"\n",
"(at nearly no additional cost)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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CnJD5/fimbUKzaYxVrGgC493A34vIx0IIj8fFfT7zeXHj38G/Bve3ew1dM6ZG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\nSUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ctrl = [Control(f), Control(nu)]\n",
"\n",
"dJdf, dJdnu = compute_gradient(J, ctrl, forget=False, project=True)\n",
"plot(dJdnu)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Or even solve an optimisation problem!"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Calling FFC just-in-time (JIT) compiler, this may take some time.\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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IGZHNsldFizZonf4MElHTwMrgpU067yETzAC/R1r05rPk2/7Py3eP32zZV7CRxaL09QDa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\nAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rf = ReducedFunctional(J, Control(nu))\n",
"nu_opt = minimize(rf, options={\"maxiter\": 4})\n",
"plot(nu_opt)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"## Some important dolfin-adjoint functions\n",
"\n",
"\n",
"### Functionals\n",
"*Mathematics*: \n",
"\n",
"$J = \\frac{1}{2}\\int_\\Omega u(T) \\cdot u(T) \\textrm{d}x$\n",
"\n",
"*Code*:\n",
"```python \n",
"J = Functional(0.5*inner(u, u)*dx*dt[FINISH TIME])\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"*Mathematics*: \n",
"\n",
"$J = \\frac{1}{2}\\int_0^T\\int_\\Omega u \\cdot u \\textrm{d}x\\text{d}t$\n",
"\n",
"*Code*:\n",
"```python \n",
"J = Functional(0.5*inner(u, u)*dx*dt)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"## Some important dolfin-adjoint functions\n",
"\n",
"\n",
"### Controls\n",
"```python\n",
"ctrl = Control(f)\n",
"ctrl = [Control(f), Control(g)]\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"### Compute sensitivity\n",
"```python\n",
"dJdf = compute_gradient(J, ctrl)\n",
"H = compute_hessian(J, ctrl)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"### Solve optimization problem\n",
"```python\n",
"rf = ReducedFunctional(J, ctrl)\n",
"f_opt = minimize(rf)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Some application examples"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Cahn-Hilliard equations\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"Quite a difficult problem to adjoint:\n",
"* nonlinear, time-dependent, fourth-order equation\n",
"* run in parallel (8 processors, MPI)\n",
"* checkpointing necessary (5 in memory, 10 on disk)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Willmore functional\n",
"\n",
"\\begin{align*}\n",
"W(u(t)) &= \\frac{1}{4\\epsilon} \\int_{\\Omega} \\left(\\epsilon \\nabla^2 u(t=T) - \\frac{1}{\\epsilon} \\frac{df}{dc}\\right)^2 \\ {dx}\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## dolfin-adjoint computes the gradient efficiently\n",
"\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Topology optimisation of a heat conduction problem"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"Problem: Find the material distribution that minimises the integral of the temperature when the amount of highly conducting material is limited.\n",
"\n",
"\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Formulation as an optimisation problem\n",
"\n",
"\n",
"\\begin{equation*}\n",
"min_{a} \\int_{\\Omega} fT + \\alpha \\int_{\\Omega} \\nabla a \\cdot \\nabla a\n",
"\\end{equation*}\n",
"\n",
"subject to\n",
"\n",
"\\begin{align*}\n",
" -\\mathrm{div}(k(a) \\nabla T) &= f \\qquad \\mathrm{in} \\ \\Omega \\\\\n",
" T &= 0 \\qquad \\mathrm{on} \\ \\delta \\Omega_D \\\\\n",
" (k(a) \\nabla T) &= 0 \\qquad \\mathrm{on} \\ \\delta \\Omega_N \\\\\n",
"\\end{align*} \n",
"\n",
"and to the control constraints\n",
"\n",
"\\begin{align*}\n",
" 0 \\le a(x) &\\le 1 \\qquad \\forall x \\in \\Omega \\\\\n",
" \\int_{\\Omega} a &\\le V\n",
"\\end{align*} \n",
"Implementation consists of 65 lines of code (including IO)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### 2D Solution\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### 3D Solution\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## OpenTidalFarm - Optimal tuning of tidal turbine farms\n",
"\n",
"* Optimisation of number of turbines, their location and their size \n",
"* Based on a shallow water solver in FEniCs + dolfin-adjoint\n",
"\n",
"\n",
"
\n",
"www.opentidalfarm.org\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## CBC-beat - cardiac electriophiosology with an adjoint\n",
"\n",
"* Implements the mono-domain and bi-domain solvers with various cell models (coupled PDE-ODE system)\n",
"* Implemented in FEniCS + Gortran (cell model generator for FEniCS) + dolfin-adjoint\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Data assimilation of blood flow models\n",
"\n",
"**Given MRI flow measurements, can we tune a blood flow model?**\n",
"\n",
"* Implements Navier-Stokes in FEniCS + dolfin-adjoint\n",
"* Requires carefull design of regularisation terms\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Multimesh support in FEniCs (Outlook)\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Multimesh support in FEniCs (Outlook)\n",
"\n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Multimesh support in FEniCs (Outlook)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
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voOvKm6WQy3h4GvTv1KJVbSr6k1hK6SshprL3V7FqTSq02t7IiUU0lat2Wxinay03TIKN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\nJUG3uuhpnpJQbpb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GKSSwSEtg2IGAAAuvsa/C8eKcN/qIyI1eG/8AUeHfaaA9d4rK/DOJ\n+RniJKn6+p7HxOV+HcQv4GeQcXl4r3OY+JCIlsNxcfZiWx0oaGguiLb6APdlXF/C6nylq23KuKS/\nw2p8pzbrKw4oAB8xqDZ4Z8RL5H/VGM1eHfEOv+390aYu8JPDq7sYldbBb7H0WQXUYrzsFAJuhp4w\ng7IADPoFeo7EwEl1JALYAew+guvsFoABbtifsNXQDFaCkMBPJFJ1l5JeoLqAqqrE7p2yVfVCaw6K\nF2V7CeOjafcb2V4FneuvcBJ4bbJVjlToVYpKhpv3TAFeGnfuDtzXm27iTVVF7MfMrdbgNVTSlldB\nJVzUGZdFXUUeqf8AQok03WWgWE857C7NrPsJ3mml3AeMydptbhLNq3sCd5q7HbqnhgEeiz7itcuf\nNkG6e69QT2z9ABrzW0C/C0nuG8csMN+pAN3XXqNLLpZEqb9V0RIBUuuWFOyQPYgVvsFjQmARaoYq\nQUAbA+wNY3ErvIDs0eH3/j9B/wAaM6roX8Hji9J/xIEvSeITvgNf5WeXcum/qeg4yd8Jqr+E87LL\n/uJhzUSdpJdCMdssbwg6B0dCfQe4nugGU8V8NqfKXFPFP/Lanykt1lYcUAA+W1Bs8M+Il8j/AKox\nmzwz4iXyfujTF3hJ4dNYwMGK7PoshWPUYCeADqMS9MhkAYk23sSSF0AM+gV6ggewCS79SQqwCAHs\nFA90MAF6AxK/QCQuoW+wm6rDAkJ743DfqMBL1E4qnWCTE3gBUxPfK9iYICrlt3gkuZLZWSpO8Byq\nyiOMd/QTu+7J8vqJx9QFlU119Rrd4Ek+rJKONwI9k0D2t9PUlyoaS7AQaTrH8hqPokS6gybC5VWc\njYWJZyAUHsMWwBsFjABbP3DqJ7YGrroA2As+gm3e24D3DZggewBRbwza4nTf8SKyWj/zoP1KOxxU\n74bUXp3OK2k+31OjrTvRmsbHPlv0+hb8uaot4GLdhS7HLoeoXkW+wkne4EtyrivhdT5S2+5VxXwu\np8pLdZWHFAAPltQbPDPiJfJ+6MZs8M+Il8n7o0xd4SeHToElnAxdWfRZCl2Fyp9B7jASCw6jATGt\niLtLuPLAe5G8pMdd2DSwAxBQO/cA6h7EU8slaAYn3HYAAt2GwIA9GFDYgDPci7TWCbE9vUAQxUGQ\nBDIxdrA6ANx7AJ7ANbCrsMAFfcNmMTwAdWMjG3fQkgIyt+g8h1BgH0C0MQB/QBNWCwgH0Y1sD2F0\nAbE8IaABbhVAtg3YCW2USjJKSfYS3YwLnrJxa7+hWqct19SFISVPPUtvpC2KWcKvfYfLHLdf2KwO\nNKm1BSST/Uc1Hl6X6FS7g9h6hlPFr/LanylxTxfw2p8ot1khxQAD5jUGzwz4iXyfugA0xd4SeHUI\nvcAPosklXQAABPuMAAW7D2AAGJgADEAAFDAAFS7BSAAE16see4AAZ9BN1mgABp3kYAALYW4AAJYQ\nZAAGJ7AADFYAAZ9g29wAA6DAAF1GAARd9BoAAbEtgAAeE+wo5AAJAAALaxoQAH5hgACe4xAAIGAA\nMGIAEnaK+Kf+V1PlEBLdZWHGAAPltX//2Q==\n",
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import YouTubeVideo\n",
"YouTubeVideo(\"wbdN0_9P6Hw\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Computing sensitivities\n",
"\n",
"Here, with respect to the initial condition:\n",
"\n",
"
\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Conclusion\n",
"\n",
"\n",
"*dolfin-adjoint* automates adjoints for FEniCS models. \n",
"\n",
"You can use it for:\n",
"* Sensitivity analysis\n",
"* PDE-constrained optimisation\n",
"* Stability analysis\n",
"* ...\n",
"\n",
"www.dolfin-adjoint.org\n"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11+"
},
"livereveal": {
"scroll": true,
"start_slideshow_at": "selected",
"theme": "serif"
}
},
"nbformat": 4,
"nbformat_minor": 1
}