High-throughput single-cell profiling provides an unprecedented ability to uncover the
molecular states of millions of cells. These technologies are, however, destructive to cells …

We propose a new approach to model the collective dynamics of a population of particles
evolving with time. As is often the case in challenging scientific applications, notably single …

Wasserstein gradient flow has emerged as a promising approach to solve optimization
problems over the space of probability distributions. A recent trend is to use the well-known …

Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

Gradient flows are a powerful tool for optimizing functionals in general metric spaces,
including the space of probabilities endowed with the Wasserstein metric. A typical …

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 establish that Polchinski's equation for exact renormalization group (RG) flow is
equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This …

This chapter describes techniques for the numerical resolution of optimal transport
problems. We will consider several discretizations of these problems, and we will put a …

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

Variational inference (VI) provides an appealing alternative to traditional sampling-based
approaches for implementing Bayesian inference due to its conceptual simplicity, statistical …