In this paper, we study the statistical limits of deep learning techniques for solving elliptic
partial differential equations (PDEs) from random samples using the Deep Ritz Method …

In the study of stochastic systems, the committor function describes the probability that a
system starting from an initial configuration x will reach a set B before a set A. This paper …

In recent years, several climate subsystems have been identified that may undergo a
relatively rapid transition compared to the changes in their forcing. Such transitions are rare …

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 …

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic
dynamical systems. When the event is rare in comparison with the timescales of simulation …

We propose a hierarchical tensor-network approach for approximating high-dimensional
probability density via empirical distribution. This leverages randomized singular value …

Determining the kinetic bottlenecks that make transitions between metastable states difficult
is key to understanding important physical problems like crystallization, chemical reactions …

In this paper, we introduce a sketching algorithm for constructing a tensor train
representation of a probability density from its samples. Our method deviates from the …

This work is concerned with solving high-dimensional Fokker-Planck equations with the
novel perspective that solving the PDE can be reduced to independent instances of density …

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