In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …

This chapter reviews different numerical methods for specific examples of Wasserstein
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …

We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-
linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known …

We propose a variational finite volume scheme to approximate the solutions to Wasserstein
gradient flows. The time discretization is based on an implicit linearization of the …

A second-order accurate in time, positivity-preserving, and unconditionally energy stable
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …

We introduce a new variational inference (VI) framework, called energetic variational
inference (EVI). It minimizes the VI objective function based on a prescribed energy …

We extend the energetic variational approach so it can be applied to a chemical reaction
system with general mass action kinetics. Our approach starts with an energy-dissipation …

In this paper, we present a systematic framework to derive a variational Lagrangian scheme
for porous medium type generalized diffusion equations by employing a discrete energetic …