{ "cells": [ { "cell_type": "markdown", "source": [ "# Variational problems\n", "\n", "*You are seeing the\n", "notebook output generated by\n", "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n", "[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/variational/script.jl).\n", "The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/variational/).*" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "In this example, we will numerically simulate an entropy-regularised Wasserstein gradient flow\n", "approximating the Fokker-Planck and porous medium equations.\n", "\n", "The connection between Wasserstein gradient flows and (non)-linear PDEs is due to Jordan, Kinderlehrer and Otto [^JKO98], and\n", "an easy-to-read overview of the topic is provided in Section 9.3 [^PC19]\n", "\n", "[^JKO98]: Jordan, Richard, David Kinderlehrer, and Felix Otto. \"The variational formulation of the Fokker--Planck equation.\" SIAM journal on mathematical analysis 29.1 (1998): 1-17.\n", "[^PC19]: Peyré, Gabriel, and Marco Cuturi. \"Computational optimal transport: With applications to data science.\" Foundations and Trends® in Machine Learning 11.5-6 (2019): 355-607.\n", "\n", "## Fokker-Planck equation as a $W_2$ gradient flow\n", "For a potential function $\\Psi$ and noise level $\\sigma^2$, the Fokker-Planck equation (FPE) is\n", "$$\n", "\\partial_t \\rho_t = \\nabla \\cdot (\\rho_t \\nabla \\Psi) + \\frac{\\sigma^2}{2} \\Delta \\rho_t,\n", "$$\n", "and we take no-flux (Neumann) boundary conditions.\n", "\n", "This describes the evolution of a massless particle undergoing both diffusion (with diffusivity $\\sigma^2$) and drift (along potential $\\Psi$) according to the stochastic differential equation\n", "$$\n", "dX_t = -\\nabla \\Psi(X_t) dt + \\sigma dB_t.\n", "$$\n", "The result of Jordan, Kinderlehrer and Otto (commonly referred to as the JKO theorem) states that\n", "$\\rho_t$ evolves following the 2-Wasserstein gradient flow of the Gibbs free energy functional\n", "$$\n", " F(\\rho) = \\int \\Psi d\\rho + \\int \\log(\\rho) d\\rho.\n", "$$\n", "\n", "## Implicit schemes for gradient flows\n", "In an Euclidean space, the gradient flow of a functional $F$ is simply the solution of an ordinary differential equation\n", "$$\n", " \\dfrac{dx(t)}{dt} = -\\nabla F(x(t)).\n", "$$\n", "Of course, there is a requirement that $F$ is smooth. A more general formulation of a gradient flow that allows\n", "$F$ to be non-smooth is the implicit scheme\n", "$$\n", " x_{t+\\tau} = \\operatorname{argmin}_x \\frac{1}{2} \\| x - x_t \\|_2^2 + \\tau F(x).\n", "$$\n", "As the timestep $\\tau$ shrinks, $x_t$ becomes a better and better approximation to the gradient flow of $F$.\n", "\n", "## Wasserstein gradient flow\n", "In the context of the JKO theorem, we seek $\\rho_t$ that is the gradient flow of $F$ with\n", "respect to the 2-Wasserstein distance. This can be achieved by choosing the $W_2$ metric in the implicit step:\n", "$$\n", " \\rho_{t + \\tau} = \\operatorname{argmin}_{\\rho} d_{W_2}^2(\\rho_{t}, \\rho) + \\tau F(\\rho).\n", "$$\n", "Finally, a numerical scheme for computing this gradient flow can be developed by using the entropic regularisation\n", "of optimal transport on a discretised domain\n", "$$\n", " \\rho_{t + \\tau} = \\operatorname{argmin}_{\\rho} \\operatorname{OT}_\\varepsilon(\\rho_{t}, \\rho) + \\tau F(\\rho),\n", "$$\n", "where\n", "$$\n", " \\operatorname{OT}_\\varepsilon(\\alpha, \\beta) = \\min_{\\gamma \\in \\Pi(\\alpha, \\beta)} \\sum_{i,j} \\frac{1}{2} \\| x_i - x_j \\|_2^2 \\gamma_{ij} + \\varepsilon \\sum_{i, j} \\gamma_{ij} \\log(\\gamma_{ij}).\n", "$$\n", "Each step of this problem is a minimisation problem with respect to $\\rho$.\n", "Since we use entropic optimal transport which is differentiable, this can be solved using gradient-based methods." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## Problem setup" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using OptimalTransport\n", "using Distances\n", "using LogExpFunctions\n", "using Optim\n", "using Plots\n", "using StatsBase\n", "using ReverseDiff\n", "\n", "using LinearAlgebra\n", "using Logging" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Here, we set up the computational domain that we work on - we discretize the interval $[-1, 1]$.\n", "The natural boundary conditions to use will be Neumann (zero flux), see e.g. [^Santam2017]\n", "\n", "[^Santam2017]: Santambrogio, Filippo. \"{Euclidean, metric, and Wasserstein} gradient flows: an overview.\" Bulletin of Mathematical Sciences 7.1 (2017): 87-154." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "support = range(-1, 1; length=64)\n", "C = pairwise(SqEuclidean(), support');" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Now we set up various functionals that we will use.\n", "\n", "We define the generalised entropy (Equation (4.4) of [^Peyre2015]) as follows. For $m = 1$ this is just the \"regular\" entropy, and $m = 2$ this is squared $L_2$.\n", "\n", "[^Peyre2015]: Peyré, Gabriel. \"Entropic approximation of Wasserstein gradient flows.\" SIAM Journal on Imaging Sciences 8.4 (2015): 2323-2351." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "function E(ρ; m=1)\n", " if m == 1\n", " return sum(xlogx.(ρ)) - sum(ρ)\n", " elseif m > 1\n", " return dot(ρ, @. (ρ^(m - 1) - m) / (m - 1))\n", " end\n", "end;" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "Now define $\\psi(x)$ to be a potential energy function that has two potential wells at $x = ± 0.5$." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=1}", "image/png": 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distributions $\\rho$:\n", "$$\n", " \\Psi(\\rho) = \\int \\psi(x) \\rho(x) dx = \\langle \\psi, \\rho \\rangle .\n", "$$" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "Ψ = ψ.(support);" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "Define the time step $\\tau$ and entropic regularisation level $\\varepsilon$, and form the associated Gibbs kernel $K = e^{-C/\\varepsilon}$." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "τ = 0.05\n", "ε = 0.01\n", "K = @. exp(-C / ε);" ], "metadata": {}, "execution_count": 6 }, { "cell_type": "markdown", "source": [ "We define the (non-smooth) initial condition $\\rho_0$ in terms of step functions." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=1}", "image/png": 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H(support + 0.25) - H(support - 0.25)\n", "ρ0 = ρ0 / sum(ρ0)\n", "plot(support, ρ0; label=\"Initial condition ρ0\", color=\"blue\")" ], "metadata": {}, "execution_count": 7 }, { "cell_type": "markdown", "source": [ "`G_fpe` is the objective function for the implicit step scheme\n", "$$\n", "G_\\mathrm{fpe}(\\rho) = \\operatorname{OT}_\\varepsilon(\\rho_{t}, \\rho) + \\tau F(\\rho),\n", "$$\n", "and we seek to minimise in $\\rho$." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "function G_fpe(ρ, ρ0, τ, ε, C)\n", " return sinkhorn2(ρ, ρ0, C, ε; regularization=true, maxiter=250) + τ * (dot(Ψ, ρ) + E(ρ))\n", "end;" ], "metadata": {}, "execution_count": 8 }, { "cell_type": "markdown", "source": [ "`step` solves the implicit step problem to produce $\\rho_{t + \\tau}$ from $\\rho_t$." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "step (generic function with 1 method)" }, "metadata": {}, "execution_count": 9 } ], "cell_type": "code", "source": [ "function step(ρ0, τ, ε, C, G)\n", " # only print error messages\n", " obj = u -> G(softmax(u), ρ0, τ, ε, C)\n", " opt = with_logger(SimpleLogger(stderr, Logging.Error)) do\n", " optimize(\n", " obj,\n", " ones(size(ρ0)),\n", " LBFGS(),\n", " Optim.Options(; iterations=50, g_tol=1e-6);\n", " autodiff=:forward,\n", " )\n", " end\n", " return softmax(Optim.minimizer(opt))\n", "end" ], "metadata": {}, "execution_count": 9 }, { "cell_type": "markdown", "source": [ "Now we simulate `N = 10` iterates of the gradient flow and plot the result." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ Info: 2\n", "[ Info: 3\n", "[ Info: 4\n", "[ Info: 5\n", "[ Info: 6\n", "[ Info: 7\n", "[ Info: 8\n", "[ Info: 9\n", "[ Info: 10\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=10}", "image/png": 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"colors = range(colorant\"red\"; stop=colorant\"blue\", length=N)\n", "plot(\n", " support,\n", " ρ;\n", " title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\log(\\rho) \\rangle$\",\n", " palette=colors,\n", " legend=nothing,\n", ")" ], "metadata": {}, "execution_count": 10 }, { "cell_type": "markdown", "source": [ "## Porous medium equation\n", "\n", "The porous medium equation (PME) is the nonlinear PDE\n", "$$\n", "\\partial_t \\rho = \\nabla \\cdot (\\rho \\nabla \\Psi) + \\Delta \\rho^m,\n", "$$\n", "again with Neumann boundary conditions. The value of $m$ in the PME corresponds to picking $m$ in the generalised entropy functional.\n", "Now, we will solve the PME with $m = 2$ as a Wasserstein gradient flow." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "function G_pme(ρ, ρ0, τ, ε, C)\n", " return sinkhorn2(ρ, ρ0, C, ε; regularization=true, maxiter=250) +\n", " τ * (dot(Ψ, ρ) + E(ρ; m=2))\n", "end;" ], "metadata": {}, "execution_count": 11 }, { "cell_type": "markdown", "source": [ "set up as previously" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=10}", "image/png": 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title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\rho - 1\\rangle$\",\n", " palette=colors,\n", " legend=nothing,\n", ")" ], "metadata": {}, "execution_count": 12 }, { "cell_type": "markdown", "source": [ "## Exploiting duality\n", "\n", "The previous examples solved the minimisation problem for the implicit gradient flow step directly, involving automatic differentiation through the Sinkhorn iterations used to compute $\\operatorname{OT}_\\varepsilon(\\rho_t, \\rho)$ each time a gradient needs to be evaluated.\n", "While this is straightforward to implement, it is computationally costly.\n", "An alternative approach for convex variational problems is to proceed via the [dual problem](https://en.wikipedia.org/wiki/Duality_(optimization)).\n", "The benefit of proceeding via the dual problem is that the part of the dual minimisation problem corresponding to the (entropy-regularised) optimal transport loss is typically available in closed form. This is in contrast to the primal problem, where evaluation of the objective and its gradients requires potentially many Sinkhorn iterations.\n", "\n", "Consider a general convex and unconstrained problem. Under (usually satisfied) conditions for strong duality to hold, we have\n", "$$\n", "\\begin{aligned}\n", "&\\min_{\\rho} \\operatorname{OT}_{\\varepsilon}(\\rho_0, \\rho) + \\mathcal{F}(\\rho) \\\\\n", "&= \\min_{\\rho} \\sup_{u}\\left[\\langle \\rho, u \\rangle - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u)\\right] + \\mathcal{F}(\\rho) \\\\\n", "&= \\sup_{u} \\min_{\\rho} \\langle \\rho, u \\rangle - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\mathcal{F}(\\rho) \\\\\n", "&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\min_{\\rho} \\langle \\rho, u \\rangle + \\mathcal{F}(\\rho) \\\\\n", "&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) - \\sup_{\\rho} \\langle \\rho, -u \\rangle - \\mathcal{F}(\\rho) \\\\\n", "&= \\sup_{u} - \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) - \\mathcal{F}^*(-u).\n", "\\end{aligned}\n", "$$\n", "Thus, the dual problem is\n", "$$\n", "\\min_{u} \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\mathcal{F}^*(-u).\n", "$$\n", "\n", "The upshot here is that $u \\mapsto \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u)$ and its gradient is available in closed form. This is a known result in the literature [^CP18].\n", "\n", "[^CP18]: Cuturi, Marco, and Gabriel Peyré. “Semi-Dual Regularized Optimal Transport.” ArXiv: Learning, 2018.\n", "\n", "The formulas we state below are lifted from statements in [^Z21].\n", "\n", "[^Z21]: Zhang, Stephen Y. “A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss.” ArXiv: Machine Learning, 2021.\n", "\n", "$$\n", "\\begin{aligned}\n", "\\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) &= -\\varepsilon \\left\\langle \\rho_0, \\log\\left( \\dfrac{\\rho_0}{K e^{u/\\varepsilon}} \\right) - 1\\right\\rangle, \\\\\n", "\\nabla_u \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) &= K^\\top \\left( \\dfrac{\\rho_0}{K e^{u/\\varepsilon}} \\right) \\odot e^{u/\\varepsilon}.\n", "\\end{aligned}\n", "$$\n", "At optimality, we can recover the primal optimal point $\\rho^\\star$ from the dual optimal point $u^\\star$ following the formula\n", "$$\n", "\\rho^\\star = e^{u^\\star/\\varepsilon} \\odot K^\\top \\dfrac{\\rho_0}{K e^{u^\\star/\\varepsilon}}.\n", "$$\n", "\n", "When $\\mathcal{F}^*(\\cdot)$ is also available in closed form (this is not always the case), the dual problem has a closed form objective and can generally be solved much more efficiently than the primal problem.\n", "\n", "In the setting of the Fokker-Planck and porous medium equations, the function $\\mathcal{F}$ can be identified with\n", "\n", "$$\n", "\\mathcal{F}(\\rho) = \\tau \\left[ \\langle \\psi, \\rho \\rangle + E_m(\\rho) \\right].\n", "$$\n", "\n", "A straightforward computation shows that\n", "$$\n", "\\mathcal{F}^*(u) = \\tau E_m^*\\left( \\frac{u}{\\tau}-\\psi \\right),\n", "$$\n", "where\n", "$$\n", " E_m^*(u) = \\begin{cases}\n", " \\langle e^u, \\mathbf{1} \\rangle, & m = 1 \\\\\n", " \\sum_i \\left[ \\left( u_i + \\frac{m}{m-1} \\right) \\left( \\frac{m-1}{m} u_i + 1 \\right)^{\\frac{1}{m-1}} - \\frac{1}{m-1} \\left( \\frac{m-1}{m} u_i + 1 \\right)^{\\frac{m}{m-1}} \\right], & m > 1.\n", " \\end{cases}\n", "$$\n", "In particular, for $m = 2$ we have a simpler formula\n", "$$\n", "E_2^*(u) = \\left\\| \\frac{u}{2} + 1 \\right\\|_2^2\n", "$$\n", "\n", "We now implement $E_m^*$ for $m = 1, 2$." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "E_dual(u, m::Val{1}) = sum(exp.(u))\n", "function E_dual(u, m::Val{2})\n", " return dot(u / 2 .+ 1, u / 2 .+ 1)\n", "end;" ], "metadata": {}, "execution_count": 13 }, { "cell_type": "markdown", "source": [ "So, the dual problem we are dealing with reads\n", "$$\n", "\\min_{u} \\operatorname{OT}^*_{\\varepsilon}(\\rho_0, u) + \\tau E_m^*\\left( \\frac{-u}{\\tau}-\\psi \\right),\n", "$$\n", "and we can thus set up `G_dual_fpe`, the dual objective." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "function G_dual_fpe(u, ρ0, τ, ε, K)\n", " return OptimalTransport.Dual.ot_entropic_semidual(ρ0, u, ε, K) +\n", " τ * E_dual(-u / τ - Ψ, Val(1))\n", "end;" ], "metadata": {}, "execution_count": 14 }, { "cell_type": "markdown", "source": [ "Now we set up `step` as previously, except this time we need to convert from the optimal dual variable $u^\\star$ to the primal variable $\\rho^\\star$. In the code, this is handled by `getprimal_ot_entropic_semidual`. We use `ReverseDiff` in this problem." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "function step(ρ0, τ, ε, K, G)\n", " obj = u -> G(u, ρ0, τ, ε, K)\n", " opt = optimize(\n", " obj,\n", " (∇, u) -> ReverseDiff.gradient!(∇, obj, u),\n", " zeros(size(ρ0)),\n", " LBFGS(),\n", " Optim.Options(; iterations=250, g_tol=1e-6),\n", " )\n", " return OptimalTransport.Dual.getprimal_ot_entropic_semidual(\n", " ρ0, Optim.minimizer(opt), ε, K\n", " )\n", "end;" ], "metadata": {}, "execution_count": 15 }, { "cell_type": "markdown", "source": [ "Now we can solve the dual problem as previously, and we note that the dual formulation is solved an order of magnitude faster than the primal formulation." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=10}", "image/png": 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length=N)\n", "plot(\n", " support,\n", " ρ;\n", " title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\log(\\rho) \\rangle$\",\n", " palette=colors,\n", " legend=nothing,\n", ")" ], "metadata": {}, "execution_count": 16 }, { "cell_type": "markdown", "source": [ "Setting `m = 2`, we can simulate instead the porous medium equation." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ Info: 2\n", "[ Info: 3\n", "[ Info: 4\n", "[ Info: 5\n", "[ Info: 6\n", "[ Info: 7\n", "[ Info: 8\n", "[ Info: 9\n", "[ Info: 10\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=10}", "image/png": 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"ρ[:, 1] = ρ0\n", "for i in 2:N\n", " @info i\n", " ρ[:, i] = step(ρ[:, i - 1], τ, ε, K, G_dual_pme)\n", "end\n", "colors = range(colorant\"red\"; stop=colorant\"blue\", length=N)\n", "plot(\n", " support,\n", " ρ;\n", " title=raw\"$F(\\rho) = \\langle \\psi, \\rho \\rangle + \\langle \\rho, \\rho - 1\\rangle$\",\n", " palette=colors,\n", " legend=nothing,\n", ")" ], "metadata": {}, "execution_count": 17 }, { "cell_type": "markdown", "source": [ "---\n", "\n", "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*" ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.0" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.0", "language": "julia" } }, "nbformat": 4 }