Closure problems are omnipresent when simulating multiscale systems, where some
quantities and processes cannot be fully prescribed despite their effects on the simulation's …

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-
grained particle-or agent-based simulations; these SDEs then provide useful coarse …

To investigate the impact of non-linear interactions on dynamic coarse graining, we study a
simplified model system featuring a tracer particle in a complex environment. Using a …

One important problem in constructing the reduced dynamics of molecular systems is the
accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved …

We present a numerical framework for learning unknown stochastic dynamical systems
using measurement data. Termed stochastic flow map learning (sFML), the new framework …

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 …

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are
profound problems. In this article, we propose a data-driven framework combining Reservoir …

We present a novel machine learning approach to reduce the dimensionality of state
variables in stratified turbulent flows governed by the Navier–Stokes equations in the …

The intricate process of bubble growth dynamics involves a broad spectrum of physical
phenomena from microscale mechanics of bubble formation to macroscale interplay …

This paper introduces an innovative data-driven approach to uncertainty quantification (UQ)
in complex engineering designs based on polynomial chaos expansion (PCE) and least …