We present a time-dependent variational method to learn the mechanisms of equilibrium
reactive processes and efficiently evaluate their rates within a transition path ensemble. This …

We formulate a class of mean field games on a finite state space with variational principles
resembling those in continuous-state mean field games. We construct a controlled continuity …

Many complex real world phenomena exhibit abrupt, intermittent, or jumping behaviors,
which are more suitable to be described by stochastic differential equations under non …

Most biochemical reactions in living cells are open systems interacting with environment
through chemostats to exchange both energy and materials. At a mesoscopic scale, the …

We study a class of variational problems for regularized conservation laws with Lax's
entropy-entropy flux pairs. We first introduce a modified optimal transport space based on …

In this paper, we construct structure preserving schemes for solving Fokker–Planck
equations associated with irreversible processes. The proposed method is first order in time …

This paper reinterprets the Freidlin–Wentzell variational construction of the rate function in
the large deviation principle for invariant measures from the weak KAM perspective …

Many processes in nature such as conformal changes in biomolecules and clusters of
interacting particles, genetic switches, mechanical or electromechanical oscillators with …

Transition path theory (TPT) is a mathematical framework for quantifying rare transition
events between a pair of selected metastable states and. Central to TPT is the committor …

Background Delta radiomics is a high‐throughput computational technique used to describe
quantitative changes in serial, time‐series imaging by considering the relative change in …