Klaus Hasselmann's revolutionary intuition in climate science was to use the stochasticity
associated with fast weather processes to probe the slow dynamics of the climate system …

Most quantum theorists are familiar with different ways of describing the effective quantum
dynamics of a system coupled to external degrees of freedom, such as the Born-Markov …

A Wiener path integral variational formulation with free boundaries is developed for
determining the stochastic response of high-dimensional nonlinear dynamical systems in a …

We present a new rank-adaptive tensor method to compute the numerical solution of high-
dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series …

Generalized quantum master equations (GQMEs) are an important tool in modeling
chemical and physical processes. For a large number of problems, it has been shown that …

Reduced models of nonlinear dynamical systems require closure, or the modelling of the
unresolved modes. The Mori–Zwanzig procedure can be used to derive formally closed …

We present a general numerical approach for constructing governing equations for unknown
dynamical systems when data on only a subset of the state variables are available. The …

In this paper, we propose using LSTM-RNNs (Long Short-Term Memory-Recurrent Neural
Networks) to learn and represent nonlinear integral operators that appear in nonlinear …

Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly
expanding range of mathematical and computational applications due to the ability of such …

We present a method for the data-driven learning of physical phenomena whose evolution
in time depends on history terms. It is well known that a Mori-Zwanzig-type projection …