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 …

Inspired by recent work on minimizers and gradient flows of constrained interaction
energies, we prove that these energies arise as the slow diffusion limit of well-known …

We propose an easy-to-implement iterative method for resolving the implicit (or semi-
implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the …

In this paper, we characterize a degenerate PDE as the gradient flow in the space of
nonnegative measures endowed with an optimal transport-growth metric. The PDE of …

We introduce a novel variant of the JKO scheme to approximate Darcy's law with a pressure
dependent source term. By introducing a new variable that implicitly controls the source …

We study nonlinear degenerate parabolic equations of Fokker--Planck type that can be
viewed as gradient flows with respect to the recently introduced spherical Hellinger …

The recently developed Particle-based Variational Inference (ParVI) methods drive the
empirical distribution of a set of\emph {fixed-weight} particles towards a given target …

We consider the idealized setting of gradient flow on the population risk for infinitely wide
two-layer ReLU neural networks (without bias), and study the effect of symmetries on the …

In this paper, we apply the Wasserstein-Fisher-Rao (WFR) metric from the unbalanced
optimal transport theory to the earthquake location problem. Compared with the quadratic …

The Wasserstein gradient flow structure of the partial differential equation system governing
multiphase flows in porous media was recently highlighted in Cancès et al.[Anal. PDE10 (8) …