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Numerical Study of a Particle Method for Gradient Flows

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arxiv 1512.03029 v3 pith:JEM73GI2 submitted 2015-12-09 math.AP cs.NAmath.NA

J. A. Carrillo , Y. Huang , F. S. Patacchini , G. Wolansky This is my paper · ORCID
classification math.APcs.NAmath.NA
keywords gradientmethodparticlediscretisationflowsnumericalaggregation-diffusionballs
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We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserves the gradient flow structure at the particle level, and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-diffusion equations.

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Cited by 1 Pith paper

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  1. Machine-Learned Sampling of Conditioned Path Measures

    stat.ML 2025-06 conditional novelty 6.0 of 10

    Two new algorithm families (controlled transport on path space and Wasserstein/JKO density evolution) for sampling posterior path measures without trajectory data, with theoretical consistency equations and toy experiments.

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