{ "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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bW2kHAQAAqUpLSxs0aJDUXo65RaimpmZvb4/RUQAAhcLn8x8+fOji4iK1V2RuERJCBg0alJ6eTjsFAABIT0FBgZGRkYGBgdRekdFF6ObmlpGRQTsFAABIT0ZGhjTHRQnDixBHhAAAiiY9Pd3NzU2ar4giBAAABklPT8cR4d+srKyam5tra2tpBwEAACnB0Og/KCkpubi4ZGZm0g4CAADS0N7eXlhYKM2r6QnDi5AQ4ubmhtFRAAAFkZWVZWtrq66uLs0XZXoR4jQhAIDikP5MGSITRYgrKAAAFIT0Z8oQmSjC9PR0gUBAOwgAAEic9GfKEOYXYd++fbW1tUtLS2kHAQAAicPQ6MvhNCEAgCJoaGior6+3traW8uuiCAEAgBHS09NdXV2VlJSk/LoyUIRYcRQAQBFQmSlDZKIIcUQIAKAIqMyUITJRhC4uLjk5ORwOh3YQAACQICozZYhMFKGWlpalpWVOTg7tIAAAIEGZmZkowlfCZfUAAPKttLRUXV3d2NhY+i8tG0WIFUcBAOQbrZkyRFaKEPNlAADkG62ZMkSGihBDowAAcozWTBkiK0VoZ2dXWVnZ1NREOwgAAEgEhkZfQ0VFxdHR8eHDh7SDAACA+HG53MePHzs7O1N5ddkoQoLThAAA8is3N9fCwkJHR4fKq8tSEeI0IQCAXKJ4gpDIUBHiCgoAAHlF8QQhkaEiHDRoUFpaGu0UAAAgfihCkZibm/P5/CdPntAOAgAAYkbxIkIiQ0VIMDoKACCPWlpaysvL7e3taQWQpSLEfBkAAPmTmZnp6OiooqJCK4AsFSGOCAEA5A/dE4REtooQlxICAMgfuicIicwV4cOHD/l8Pu0gAAAgNnQvIiSyVYR6enpGRkaFhYW0gwAAgNhgaLR7cJoQAECeVFdXs9lsCwsLihlkrAhxmhAAQJ6kpaXRPRwkPSjClJSUO3fuSCKKKHAFBQCAPKE+U4Z0twjT0tJGjhy5ZMkSCaV5LRwRAgDIE+ozZUi3ipDL5YaFhS1dulRyaV7LycmpsLCwvb2dYgYAABAX6jNlSLeKcPv27aNGjfLw8JBcmtdSU1OzsbHJysqimAEAAMRCIBA8evTI1dWVbgxVEffLzs6OjIxksVixsbGv3ZnFYn377bfCbQsLizlz5nSxM4fDIYQIBAIRk7i6uj548MDFxUXE/UF0wvdCSUmJdhAgPB6Pw+Goqor6HQqSIxAIOByO8LsDxKugoEBfX19HR0f0L2933wtVVdXX/kwT6duMz+cvWrRo586dIt4+uLW1tba2Vritq6vL4/G62JnH4ykrK4v+w9fV1TU9Pb3r54SeEX5V8bVlAt5faAcBIhAI8F5ISFpampubW7e+tt19L1RUVMRThDdv3nz06FF0dHR0dHRubm5JSUlYWNjOnTs1NDReur+/v/+2bdtETCkQCNTU1ET/zffNN9/cu3evpqamiPuD6JSVlQkh6urqtIPAn78g4v85EwiLEO+FJGRnZ7u7u3fra8vhcMT+XohUP46Ojj/99JNwW1NTMz8/PyAggNZK4Zg4CgAgH9LT04ODg2mnEK0ITUxMZsyYIdzmcDjXr1/v+FD6rK2tGxoa6uvrDQwMaGUAAIDey8jIWLt2Le0U3b+g3sfH56uvvpJEFBEpKSm5ubmlpqZSzAAAAL3U2tpaUFDg6OhIO0j3i9De3n7atGmSiCI6Dw+Pe/fu0c0AAAC9kZqa6uTk9Kq5JtIkY2uNCnl6eqIIAQBk2r179zw9PWmnIARFCAAAVKAIe8XFxaWsrOzZs2e0gwAAQA+hCHtFRUXFzc3twYMHtIMAAEBPtLW15ebmUl9uW0gmi5BgdBQAQJalpaU5OjoyZJkCGS7ClJQU2ikAAKAn7t27R/cWDp3JahHiCgoAANnFnBOERHaL0NXVtbi4uLGxkXYQAADoNhShGKiqqrq6umJ9GQAAmdPe3v748WPq9+PtIKtFSDBfBgBANqWlpQ0cOFBLS4t2kD+hCAEAQKoYNS5KUIQAACBlKEKxcXV1LSoqampqoh0EAAC6AUUoNmpqai4uLpgvAwAgQ9hsdnZ2NnNmyhCZLkKC0VEAAFmTlpZmb2+vra1NO8jfUIQAACA9KSkpzFlTRghFCAAA0sO0E4RE1ovQzc2tsLCwubmZdhAAABAJilDM1NTUnJ2dMV8GAEAmsNnsR48eubu70w7yD7JdhASjowAAsiMjI8PW1lZHR4d2kH+Q+SL08PDA/ZgAAGQCA8dFiRwUIY4IAQBkBYpQIgYNGpSXl9fS0kI7CAAAvAaKUCLU1dWdnJzS0tJoBwEAgK5wOJxHjx4NHjyYdpDnyXwREoyOAgDIgoyMDGtra6bNlCEoQgAAkI6UlBQGjosSFCEAAEjHvXv3mLa4mpA8FKG7u3teXl5rayvtIAAA8ErMnClD5KMI1dXVHRwcMF8GAICxuFxuZmYmA2fKEPkoQoLRUQAAZsvMzLSystLT06Md5CVQhAAAIHGMHRclKEIAAJACFKHEubu75+TkYL4MAAAzoQglTkNDw8HBIT09nXYQAAB4Ho/Hy8zMfPPNN2kHeTk5KUJCiKenJ25DAQDAQJmZmZaWlsycKUPkqQg9PDxwmhAAgIGYPC5K5KkIMV8GAICZUlJSmLmmjJD8FOHgwYOzs7Pb2tpoBwEAgH/AEaGUaGpq2tvbZ2Rk0A4CAAB/4/F46enpjJ0pQ+SpCAlGRwEAmOfRo0fm5ub6+vq0g7ySXBWhl5cXi8WinQIAAP6WnJzs5eVFO0VX5KoI/fz8kpKSaKcAAIC/3bx508/Pj3aKrshVEQ4aNKi8vLy2tpZ2EAAA+FNSUhKKUHpUVFS8vb1v3bpFOwgAABBCSH19fUlJyaBBg2gH6YpcFSEhxM/PD0UIAMAQSUlJPj4+qqqqtIN0RQ6L8ObNm7RTAAAAIYQkJSUNHz6cdorXkLci9PX1TU5O5nA4tIMAAABJSkry9fWlneI15K0I+/TpY2Njk5qaSjsIAICi43K59+7dGzp0KO0gryFvRUgIGT58OC6iAACgLjU19Y033jA0NKQd5DW6V4Tt7e08Hk9CUcTF19cXRQgAQB3zryAUErUIL1y4MGDAgL59++rp6QUGBpaUlEg0Vm8MHz48MTGRdgoAAEV369YtuSpCV1fXpKSk5ubmmpoaIyOjjz/+WKKxesPOzo7H4zG5qgEAFIG8HREOGDBgwIABhBAtLa3x48dXVFRIMlVv+fr64iIKAACKysrK2tvb7e3taQd5vW5c5NjY2Hj+/Pni4uLff/9969atXezZ3t5eV1f35wuoqurp6fUqY/cJL6ufNWuWlF8XAACEEhMTZeJwkHSrCFtaWi5dulRZWSkQCHR0dLrY87fffjt48KBw28vL6+TJk13s3NraqqamJt51B958881Dhw41NjaK8TkVAZvNJoSoq6vTDgKEx+Ox2Wwul0s7CBCBQNDS0iIQCGgHkTFXr1719PQU+8/hpqambu2vra2toqLS9T5KPXh3jxw5snr16uLi4pf+7fbt258+fbpt2zYRn00SRdje3m5kZFRZWamrqyvGp5V7KELmEBahlpYW7SBABAJBc3Mzfph0l7e3944dO8S+rExjY6PYRxl7ch2hi4vL06dPmXwdhYaGxuDBg3FvQgAAKlpbW7Oysjw9PWkHEYmoRXjs2LHr16+XlJTcvXv3008/nThx4msPNunCZfUAALTcuXPH3d1dU1OTdhCRiDogyeFwvvrqq9LS0r59+wYGBn755ZcSjdV7vr6++/fvp50CAEARycqFE0KiFuHcuXPnzp0r0SjiNXz48AULFvD5fGVlOVxGDgCAyW7durVgwQLaKUQltyVhYmJiZGSUlZVFOwgAgGIRCAS3b99m/k0nOshtERLcmxAAgIZHjx4ZGBiYmprSDiIqOS9C3K0eAEDKkpKSZOgEIZH7IsQRIQCAlKEIGcTV1fXJkydPnz6lHQQAQIGgCBlEWVl56NChGB0FAJCampqayspKV1dX2kG6QZ6LkBDi5+eHy+oBAKQmKSlp2LBhDF9x5TkoQgAAEJukpCQZunBCSM6LcNiwYffv3xeuJQ0AAJImcycIidwXoa6urr29/f3792kHAQCQfxwOJyUlxcfHh3aQ7pHzIiSEDB8+HBdRAABIQUpKir29vb6+Pu0g3SP/Rejr64uJowAAUiCL46JEEYpw+PDhiYmJtFMAAMg/FCFDWVtbq6ioFBQU0A4CACDnbt26hSJkKF9fX1xEAQAgUYWFhVwu18bGhnaQblOIIsTq2wAAkpaUlDRixAjaKXpCUYoQE0cBACRKRk8QEgUpwiFDhuTn59fV1dEOAgAgt27cuDF8+HDaKXpCIYpQXV3dz8/v6tWrtIMAAMinJ0+elJSUeHl50Q7SEwpRhISQcePGXbp0iXYKAAD5dOnSpVGjRsnWWtsdUIQAANBbly5dGjduHO0UPaQoRTh48OCamprS0lLaQQAA5BCKUAYoKyuPHj0aB4UAAGKXm5vLZrOdnZ1pB+khRSlCgtFRAADJuHTpUkBAAO0UPadARRgQEIAiBAAQO5keFyUKVYR2dnbq6uqPHj2iHQQAQH7w+fyrV6+OHTuWdpCeU6AiJBgdBQAQt9TUVCMjI0tLS9pBeg5FCAAAPZeQkCDT46JEAYvw6tWrPB6PdhAAADkh6ycIiaIVoYmJyYABA+7du0c7CACAPGCz2bdu3Ro9ejTtIL2iWEVICBk3blxCQgLtFAAA8uDWrVtOTk6Ghoa0g/SKIhYhThMCAIiFHIyLEgUswlGjRrFYrNbWVtpBAABknhzMlCEKWIR6enru7u64Ty8AQC81NjZmZGTI6M14O1O4IiQYHQUAEIerV6/6+PhoaWnRDtJbKEIAAOgJ+ThBSBSzCIcNG5adnV1bW0s7CACADJP1tbY7KGIRqqur+/n5Xbt2jXYQAABZVVVVVVZW5uHhQTuIGChiERKMjgIA9E5CQsLo0aNVVFRoBxEDBS3CgIAAXFYPANBjcnOCkChsEQ4ePLi2trakpIR2EAAAmXTlyhX5OEFIFLYIlZSUxowZc/nyZdpBAABkT05ODpvNdnR0pB1EPBS0CAlOEwIA9NSlS5cCAwNppxAbRS9CgUBAOwgAgIyRpxOERJGL0M7OTkNDIysri3YQAABZwufzr169OmbMGNpBxEZxi5AQMnbsWMwdBQDolvv37xsbG1taWtIOIjYKXYQ4TQgA0F1ys6BMB0UvwmvXrvF4PNpBAABkhpydICQKXoQmJiZWVlYsFot2EAAA2dDe3n7r1q1Ro0bRDiJOCl2EhJAJEyacP3+edgoAANlw7do1d3d3AwMD2kHESdQirKmp+fHHH0NDQ+fMmbN3714OhyPRWFITEhISGxtLOwUAgGyIjY2dNGkS7RRiJmoRnjt3LikpKTAwMCQkZOfOnStXrpRoLKnx9fWtqqoqKCigHQQAgOkEAsHp06dDQkJoBxEzVRH3Cw0NDQ0NFW6bmJhMnz59z549EkslPcrKyu+8886ZM2dWrFhBOwsAAKOlpKTo6OjIzcpqHXpyjrC4uNjMzEzsUWjB6CgAgCji4uLk73CQiH5E2KGysvLLL7/cvXt3F/vExMQkJycLt52dnbdu3drFzq2trWpqaqqq3U4iLn5+fvPmzSstLZWz0789wGazCSHq6uq0gwDh8XhsNhvX9jCBQCBoaWmhnYIR/ve///3www9NTU0UMzQ3NyspKYm+v7a2trLyaw75ulc/NTU148ePX7p06dSpU7vYzcfHZ+HChcJtAwMDXV3dLnZWUVGhW4S6urqjR4++cePG7NmzaWVgCBQhcwiLUEtLi3YQIAKBQElJqeufY4qgqKioqqqK+s14BQKB2N+LbtRPXV3d+PHjg4KCvv766673tLKykq11B4SjoyhCAIBXiY2NnThxonzckv45op4jbGhomDBhgr+//5YtWyQaiIrg4OA//vhDeDwEAAAviouLk78LJ4RELcIDBw6wWKzY2Fi7vzI7IawAACAASURBVLS2tko0mTSZmJg4Oztfu3aNdhAAACZqaGhITk6WraE+0Yk6NBoWFjZv3rzOj2hqakogDzXC0VF5utUkAIC4nD17dtSoUdra2rSDSISoR4SampqG/9SteTvMN2nSpFOnTuE+vQAAL5LjcVGCtUY7ODk56erqPnjwgHYQAABm4XA48fHx77zzDu0gkoIi/BuurAcAeNGVK1ecnJxMTU1pB5EUFOHfQkJC4uLiaKcAAGAW+R4XJSjCzvz8/MrLywsLC2kHAQBgkLNnz8rlymodUIR/61iAm3YQAACmSElJUVVVdXJyoh1EglCE/4DThAAAncXFxU2ZMoV2CslCEf7D+PHjWSxWfX097SAAAIwQGxsr3+OiBEX4HG1tbX9//wsXLtAOAgBAX3FxcWlpqa+vL+0gkoUifB5GRwEAhOLi4oKDg+Vyoe3OUITPCwkJuXjxIhbgBgBQhHFRgiJ8kYmJiZOT0/Xr12kHAQCgqaGhgcViKcIKzCjCl8DoKADA+fPn/f39dXR0aAeROBThS0yaNCkuLg4LcAOAIouLi1OEcVGCInwpZ2dnTU3N1NRU2kEAAOjgcDgXL16cOHEi7SDSgCJ8OYyOAoAiu3btmqOjoxwvtN0ZivDlpkyZcuLECdopAADoOHHixOTJk2mnkBIU4cv5+vo2NzdjdBQAFBCbzT5x4sTMmTNpB5ESFOHLKSkpzZkzJzIyknYQAABpO3v2rJubm7W1Ne0gUoIifKV58+YdOXKEx+PRDgIAIFWRkZGhoaG0U0gPivCVBg4caGlpeenSJdpBAACkp66u7vLly1OnTqUdRHpQhF2ZO3duVFQU7RQAANJz/PjxCRMm6Ovr0w4iPSjCrsyaNev06dNNTU20gwAASImijYsSFGHXjI2NR4wYcerUKdpBAACkobCwMDc3d/z48bSDSBWK8DVCQ0MxdxQAFMTBgwffffddNTU12kGkCkX4GiEhIcnJyWVlZbSDAABI3OHDhxVtXJSgCF9LU1NzypQpR48epR0EAECybt++LRAIvLy8aAeRNhTh62HuKAAogqioqHnz5tFOQQGK8PVGjRpVX1+fnp5OOwgAgKRwOJzjx4/PmTOHdhAKUISvp6SkNHv2bBwUAoAcO3/+vLOzs42NDe0gFKAIRRIaGhoVFYXl1gBAXing5YMdUIQicXZ2NjMzu3r1Ku0gAADi19DQcOnSpenTp9MOQgeKUFS4oBAA5NXx48cDAgIMDAxoB6EDRSiq2bNnx8bGYrk1AJA/ijwuSlCEojMxMfHz84uLi6MdBABAnIqKih49evTWW2/RDkINirAbcEEhAMifqKiod999V11dnXYQalCE3TB58uS7d+9WVlbSDgIAIDZRUVGKPC5KUITdoqWlFRwcjOXWAEBusFgsLpfr4+NDOwhNKMLuwdxRAJAnkZGR8+bNU1JSoh2EJhRh94wePbq6uvrBgwe0gwAA9FZbW9uxY8fmzp1LOwhlKMLuUVZWXrp06c6dO2kHAQDorUOHDg0dOlQxl1XrTJV2ANkTFhZmb29fVVXVv39/2lkAAHpu165d33//Pe0U9OGIsNsMDQ2nT5/+yy+/0A4CANBzV65c4XK5Y8eOpR2EPhRhT4SHh+/Zs4fNZtMOAgDQQxEREeHh4Qo+TUYIRdgTLi4uLi4u0dHRtIMAAPREYWHhzZs3FfPugy9CEfZQeHj4Dz/8QDsFAEBPRERELFy4UEdHh3YQRkAR9lBQUFBTU9OtW7doBwEA6J7GxsbIyMhly5bRDsIUKMIeUlJSWr58eUREBO0gAADdc+DAgYCAgAEDBtAOwhQowp774IMPEhISSkpKaAcBABCVQCDYvXt3eHg47SAMgiLsOT09vdDQ0D179tAOAgAgqnPnzunq6vr6+tIOwiDdK8LS0tJ79+61t7dLKI3MCQ8P379/f3NzM+0gAAAiiYiIWLVqFe0UzCJqET59+tTU1NTFxcXLy6usrEyimWSItbW1r6/v4cOHaQcBAHi9hw8fZmZmzpgxg3YQZhG1CPv06XP16tUnT55INI0sCg8Pj4iIEAgEtIMAALxGRETEkiVLFPkevC8lahFqaGg4OTkpK+Oc4vPGjh2rqqp6+fJl2kEAALpSV1cXExOzePFi2kEYRyKLbqelpf3888/CbVNT0+Dg4C525vF4ysrKMr3Mz/Lly3fs2DF69GjaQXqLx+N1/Al08f5COwgQgUAgH+/Fzz//HBIS0q9fP5n+t3T3vRClXyRShFVVVSwWS7hta2s7fvz4LnZub2/n8/ky/cZMnz59/fr1GRkZAwcOpJ2lV4Srp2KYlwl4PB6bzcYYDBMIBIL29nY1NTXaQXqFy+Xu2bPn+PHjsj7bkc1md+ufoKmpSacIAwMDt23bJuLOSkpKampqqqoyfEMobW3tBQsW/Pe//92xYwftLL0ifBdw/oAJeDyeqqqqlpYW7SBABAKBQCDQ1tamHaRXjh8/bmtrO2zYMNpBeovH44n9vcDvm+KxfPnyyMjIhoYG2kEAAF5CeK8J2ikYqhtF+H//93/r1q0jhGzbtm3NmjW4CVFn5ubmb7311q+//ko7CADA8+7evVteXh4SEkI7CEN1Y0DSwMBAU1Pzu+++E34o09NbJGHt2rUBAQGLFi3S09OjnQUA4G/r1q378ssvVVRUaAdhqG4UIQ6ru+bm5hYYGLhjx47169fTzgIA8Kdr164VFRV9+OGHtIMwF84RitPmzZsjIiKw7AAAMMeaNWs2b94s67NeJQpFKE7W1tazZs0SfcYsAIBEnTx5sqWlBWuqdQ1FKGZff/31wYMHcW8mAKCOx+OtX79+69atuCC1a/jqiJmJicmiRYs2bdpEOwgAKLrIyEgjI6MJEybQDsJ0KELx++KLL+Li4h49ekQ7CAAoLjabvXnz5o55/tAFFKH46evrf/LJJxs3bqQdBAAU1549e9zc3Pz8/GgHkQEyvLAZk61cudLBweHu3bs+Pj60swCAwmlqatq6dev58+dpB5ENOCKUCC0trXXr1n399de0gwCAIvrPf/4TEBAwePBg2kFkA4pQUhYsWJCXl4f7FAKAlFVXV+/atWvDhg20g8gMFKGkqKmpbdq06csvv8RdjQBAmrZs2TJr1iw7OzvaQWQGilCCZs2axeFw4uLiaAcBAEVRVlZ28OBB4Q0SQEQoQglSUlLavHnzunXrZPq2wwAgQzZs2BAWFmZqako7iCxBEUpWUFCQsbHxoUOHaAcBAPn3+PHjuLi4Tz/9lHYQGYMilLjNmzdv2LChqamJdhAAkHOff/75Z599ZmhoSDuIjEERStyIESNGjx69du1a2kEAQJ4dOXIkJydn5cqVtIPIHhShNOzYsSM2Nvb69eu0gwCAfKqurv7ss89+//13TU1N2llkD1aWkQZ9ff1du3YtXLgwNTVVS0uLdhygrKGh4cmTJ7W1tbW1tTU1NZ03OByOcB+BQMDn8ztuKa6kpNS3b18jI6O+fft23ujbt2///v3p/VOAKT766KO5c+d6e3vTDiKTUIRSEhIScuzYsfXr1//73/+mnQWkp6amJjc3Nzc3NycnJycnR7jNZrNNTU2fq7SBAwcaGRmpq6sLP5HP53O53M4fCpuytLQ0NTW19i/V1dUtLS329vb29vYDBw60/4ulpSW9fzRI2//+97/U1NQDBw7QDiKrUITSs3PnzkGDBk2fPn3YsGG0s4CkFBUVsVisu3fvslistLQ0Pp/fUU5vvfXWRx99ZG9vb2xs/Nrn4fF4bDZblPGDxsbGjq5NSko6ePBgTk7Os2fPXFxcvL29vb29fXx8nJycOg4uQc7U1tZ+9NFH0dHRGBTtMRSh9BgZGe3cuXP+/Pn379/X0NCgHQfEo6amRlh7wv5TVVUVds/atWuHDBnSr18/SQfQ09MbMmTIkCFDOj/Y1NSUnp7OYrEuX768devWioqKIUOGCIMNHTrUyspK0qlAaj7++OOZM2fiLhO9oST2BcC2b9/+9OnTbdu2ibh/a2urmpqaqqqiVPKMGTMGDhz47bff0g7yEmw2mxDSMRwHr9Le3n7z5s34+Pj4+Pjc3FxhwQgPvywsLMTyEqIfEYqivr4+OTlZWNi3b9/W0dEJDAwMDAwcO3asgYGBWF5CjgkEgubmZl1dXdpBXuLs2bPh4eFpaWna2tq0s0hJY2Ojnp6eeJ9TUeqHOfbs2ePu7j5lyhSc1pY5+fn5CX+xtbUNCAj47rvv/P39mf+rg4GBQUBAQEBAgPBD4T/k6NGjCxYssLOzE/6VTPxDoLOGhoalS5f+9ttvitOCEoIjQgoOHz68detWFovFtJ87OCJ8EZfLvXr16okTJ+Li4jQ1NQMDA8ePHz9mzBhJX7Ms3iPCV2lvb09MTBQe2ubl5Y0fP37atGlBQUHMPPqhhbFHhAsXLtTQ0Ni9ezftIFIliSNCFCEdkyZNGjJkCNPuYo8i7MBmsy9dunTixInY2FgbG5vp06dPnTrV3t5eagGkU4SdPX36NC4u7sSJEzdv3hwzZsy0adOCg4MxcEqYWoTx8fGLFy9OS0sTeyswHIpQfpSXlw8ZMiQ+Pt7d3Z12lr+hCNva2i5evHjixImzZ886OztPmzZt2rRpVKaWSL8IO9TX158+ffrEiRNXrlwZMWLEtGnTJk2aZGRkJP0kDMHAImxsbHR3d9+3b19gYCDtLNImiSLEyjJ0mJubb9269cMPP+RyubSzACGEJCUlLVmyxNLSMiIiYujQoenp6YmJiatWrVLACZYGBgahoaGnTp0qLS0NDQ09f/68vb391KlTY2NjO673B7rWrFkzbtw4BWxBCUERUvPBBx+YmZl9/vnntIMotOLi4m+++cbR0XHhwoXW1tYPHjy4fPny8uXLzc3NaUejT09Pb9asWdHR0UVFRRMnTvzPf/5jaWkZHh5+79492tEUWnR09Llz577//nvaQeQHipCmw4cPJyQk7Nmzh3YQhdPa2hodHR0cHOzh4VFSUvLrr79mZmauWbMGC7K8VJ8+febPn3/t2rXk5GRzc/NZs2a5uLhs3LixqKiIdjSFk5KSsmLFilOnTunr69POIj9QhDT16dPn1KlTmzdvTkhIoJ1FUTx48GDJkiUWFhaRkZEffPBBWVnZ3r17R4wYoaSkRDuaDBgwYMDq1asfP368d+/e0tLSIUOGTJ48+cKFC3w+n3Y0hVBSUjJp0qRffvll8ODBtLPIFRQhZXZ2dsePH58zZ05mZibtLPKsvb09Ojo6MDAwKCjIwMAgNTU1Li5u2rRpWOKnB5SUlEaOHLl///7y8vL33nvvm2++sbKy2rhx45MnT2hHk2ctLS3Tpk1btWpVcHAw7SzyBkVI34gRI7Zv3x4SEvL06VPaWeRQTk7OmjVrBgwYsG/fvsWLFxcVFX333XcDBgygnUseaGpqzpgxIzExMTY2tqKiwsnJaebMmQkJCWKfiw58Pn/OnDlubm6ffPIJ7SxyCEXICO+///7MmTNnzJghvIABeo/L5cbExIwdO9bf319FReXu3bvx8fEzZsxQtAt1pMPT03Pv3r35+fkjR478+OOPXV1dd+3a9ezZM9q55MeaNWuePXu2d+9e2kHkE4qQKf71r38ZGRktWbKEdhCZV1NTs3XrVjs7u4iIiCVLlhQXF//rX/+ytramnUv+GRgYrFixIiMj4+eff05MTLSxsQkPD8/JyaGdS+b99ttvsbGxMTExampqtLPIJxQhUygrK0dFRWVmZoq+FgE8Jzs7Ozw8fODAgffu3Tt27NiNGzdmzpyJnx3S5+/vf+zYsczMTENDwxEjRgQGBp4+fRrjpT1z48aNdevWnT59um/fvrSzyC0UIYNoaWmdOnVq9+7dp06dop1FlvD5/NOnTwcGBo4ZM0ZLSysjI+P48eO46SN1pqamGzduLC4uXrx48bfffuvg4LB169b6+nrauWRJfn7+u+++GxUV5eDgQDuLPEMRMouZmdnJkyfDwsLu379PO4sMaGho+M9//mNnZ/fdd98tWLBAOBEG18IzioaGxowZM27duvXrr7+yWCx7e/vPPvussLCQdi4ZUFdX984772zatGncuHG0s8g5FCHjCOcdvPPOO7du3aKdhblyc3PDw8NtbW1TUlKio6Nv3rw5a9YsjIIymb+/f0xMTEpKirKysre394wZM27evEk7FHOVl5ePGTNmypQpCxcupJ1F/qEImWjy5MlRUVGTJk2Kjo6mnYVxEhMTZ86cKRz5fPDgQVRUlJeXF+1QICorK6tt27aVlJQEBwcvXrzY09Nz3759bW1ttHMxy6NHj4YPHz558uQtW7bQzqIQUIQMNW7cuPPnz3/88cdYgE2ovb39wIEDQ4YMWbJkSWBgYElJSUREBC4HlFGamprz5s1LT0/ftGlTdHS0vb39li1bqquraedihMTExDFjxmzatIlpt2mTYyhC5vL09Lxx48aOHTvWrVunyDPuKioqvv76a2tr6+PHj2/dujU9PX3RokVU7k8E4qWsrBwUFBQfH3/+/Pm8vLyBAwcuXLgwNTWVdi6aTp48OW3atMjIyNDQUNpZFAiKkNFsbW1v3bp1/fr1999/XwHvgHPv3r2wsDB3d/eqqqpLly6dO3du/PjxWBRU/gwaNGj//v0FBQWDBg0KCQnx8vI6ePCgAt6h7Mcff1y5cuX58+dxfyUpQxEyXd++fePj41tbW99++20FWaqDw+EI1wWdOXOmra1tdnb23r17XVxcaOcCyTIwMAgPD8/Pz9+wYUNkZOQbb7yxcePGmpoa2rmkQSAQbNy4MSIi4urVqx4eHrTjKBwUoQzQ1NQ8evSonZ3dmDFjKisraceRoPLy8k2bNtnY2Ozdu3fFihU5OTmrV6/GdcQKRUVFJTg4OD4+/tSpU8Lx0qVLl8r3eCmbzQ4NDY2Pj799+7a9vT3tOIoIRSgbVFRU9u7dO3nyZD8/v+vXr9OOI2YCgSA+Pn7atGmDBg2qrKy8cOFCQkJCSEiIsjL+fyoub2/vyMjIhw8fmpubBwcH+/n5HTx4UP7ml+bn548fP76lpSUhIcHIyIh2HAWFHzSyZP369REREaGhoQsXLqytraUdRwyqq6v//e9/Ozg4fPHFF+PHjy8qKvrpp5/c3Nxo5wKmMDU1Xb9+fUFBwerVq48cOWJlZfXZZ589fvyYdi4x4HA427ZtGzp0aHBwcExMDOZ/UYQilDHBwcEZGRk6Ojpubm6HDx+mHaeHBAJBYmJiaGjowIEDMzIyIiMj79+/HxYWpqurSzsaMJGKisqkSZPOnz9/+/ZtVVVVf3//wMDAmJgY2b1by507d7y8vK5evcpisT799FMMftCFr77s0dPTi4iIiI2N3b59+4QJE/Lz82kn6oa8vLyNGzcOHDgwLCzMw8MjLy/vwIEDWBcURGRra/vdd98VFxfPnz9/9+7dFhYWy5cvl601mJ49e7ZixYqpU6euXbv23LlzuC8KE6AIZZW3tzeLxXr77beHDRu2ceNGhv9qXF9ff/DgwcDAwKFDh1ZUVBw4cCAzM3PVqlWYCAM9oK6uPnv27CtXrty/f9/BwWHZsmVvvPHGmjVrcnNzaUd7jdOnT7u7uzc0NKSlpb377ru048CfUIQyTFVVNTw8/O7duywWy9vb+9y5c3w+n3aof2htbT116tS0adNsbGyEC+VUVlbu3bt3xIgRtKOBPLC0tAwPD79//35MTExra+vw4cNHjhy5b98+Bl50kZKSMnny5DVr1kRFRR08eBDzYhgFRSjzrK2tz549u379+o0bN9ra2n7zzTfl5eV0I1VUVPzyyy+TJk0yNTXduXPnxIkTi4qKjhw5EhQUhBvEgyR4e3tHRESUlpauXr368uXLtra2I0eO3LZt28OHD+kGa2pq2r9/v4+Pz9SpU4cPH37//n38FshA3SjCr7/+2sjIyMDAYPny5Qq46APDTZ8+/e7du+fOnWtqaho8eHBgYGB0dLSU36bMzMytW7eOGDHC0dExLi4uKCjo8ePHly9f/vDDD/v06SPNJKCY1NTUJk6cePTo0aqqqg0bNpSVlb399ts2NjZhYWGnT59ub2+XZpiHDx+uWbPGxsbm2LFjn3/+eW5u7ueff66uri7NDCAiJREXsYyLi1uxYsXNmzd1dHTGjh27aNGiZcuWvXTP7du3P336VPTbrLe2tqqpqeFAQYyampqOHDmyb9++6urqhQsXfvDBBxYWFqJ8ovBEo+jfq1wuNz09/c6dO3fu3ImPj9fR0QkODg4KCho5ciTe0F7i8XhsNhtT6nsvNTX1zJkzp0+fzs7OHjt2rK+vr4+Pj6enp46OjojPIBAImpubRZzS3NjYePz48X379lVWVi5cuHDBggW4QaZ4NTY26unpifc5RS3CKVOmeHp6fvXVV4SQgwcP7tq1i8VivXRPFCFzpKSk7N27NyYmRk9Pz8vLy8vLy9vb29PT08DA4KX7i1KE+fn5d+7cYbFYd+/eTU1Ntba29vHx8fHxGTNmDG6iLUYoQrF78uRJQkLC3bt37969m5aWZmdn5/MXV1fXLn4EdV2EbW1tqampycnJLBYrOTm5qKho7NixYWFhEyZMwEURkkCzCF1cXLZs2TJp0iRCSEpKypgxYxoaGl665/bt20tLSztuIKKqqtp1aBShFOTm5iYnJwu/Vx88eNC/f39vb28PDw9TU1N1dXV9fX1VVVV9fX1lZWVtbW0DAwMul1taWlpVVfXcnyUlJTo6Oh0/Pjw9PcX+PxKEUIQSxeFwUlNThaXIYrGKi4utrKzMzMzMzc2Ff3Zs6Ovr19fXNzQ0COuQzWY3NDRwudzq6uq0tDQWi5Wdne3k5OTt7S38XdPNzQ0/zSSKZhGamZlFRUWNGzeOEJKTk+Pg4MBms196Q/Dt27dv2rSp47+Cl5fXyZMnu3hmFKGU8fn8x48f379/PzU1tbq6msPh1NfX83i8Z8+etbe3t7S0tLS0qKmpmZmZ9e/f39zc3MTExNz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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": "1.7.1" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.1", "language": "julia" } }, "nbformat": 4 }