Optimal transport for single-cell and spatial omics
C Bunne, G Schiebinger, A Krause, A Regev… - Nature Reviews …, 2024 - nature.com
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 …
molecular states of millions of cells. These technologies are, however, destructive to cells …
Proximal optimal transport modeling of population dynamics
C Bunne, L Papaxanthos, A Krause… - International …, 2022 - proceedings.mlr.press
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 …
evolving with time. As is often the case in challenging scientific applications, notably single …
Variational Wasserstein gradient flow
J Fan, Q Zhang, A Taghvaei, Y Chen - arXiv preprint arXiv:2112.02424, 2021 - arxiv.org
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 …
problems over the space of probability distributions. A recent trend is to use the well-known …
Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
JA Carrillo, K Craig, Y Yao - Active Particles, Volume 2: Advances in …, 2019 - Springer
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 …
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …
Optimizing functionals on the space of probabilities with input convex neural networks
D Alvarez-Melis, Y Schiff, Y Mroueh - arXiv preprint arXiv:2106.00774, 2021 - arxiv.org
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 …
including the space of probabilities endowed with the Wasserstein metric. A typical …
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems
G Fu, S Osher, W Li - Journal of Computational Physics, 2023 - Elsevier
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 …
spatial discretization for initial value gradient flows in generalized optimal transport metric …
Renormalization group flow as optimal transport
J Cotler, S Rezchikov - Physical Review D, 2023 - APS
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 …
equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This …
Optimal transport: discretization and algorithms
Q Merigot, B Thibert - Handbook of numerical analysis, 2021 - Elsevier
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 …
problems. We will consider several discretizations of these problems, and we will put a …
Lagrangian schemes for Wasserstein gradient flows
JA Carrillo, D Matthes, MT Wolfram - Handbook of Numerical Analysis, 2021 - Elsevier
This chapter reviews different numerical methods for specific examples of Wasserstein
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …
gradient flows: we focus on nonlinear Fokker-Planck equations, but also discuss …
Mean field variational inference via Wasserstein gradient flow
R Yao, Y Yang - arXiv preprint arXiv:2207.08074, 2022 - arxiv.org
Variational inference (VI) provides an appealing alternative to traditional sampling-based
approaches for implementing Bayesian inference due to its conceptual simplicity, statistical …
approaches for implementing Bayesian inference due to its conceptual simplicity, statistical …