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.
Numerical Study of a Particle Method for Gradient Flows
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abstract
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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Machine-Learned Sampling of Conditioned Path Measures
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.