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Predicting the rheological behavior of associative polymers bridging colloidal particles into transient networks is fundamentally challenging because the coupled spatiotemporal scales prevent efficient molecular-fidelity modeling. We…
We specify the conditions when a manifold M embedded in an inner product space E is an invariant manifold of a stochastic differential equation (SDE) on E, linking it with the notion of second-order differential operators on M. When M is…
Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analyzing multiscale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD)…
We investigate crystal nucleation in supersaturated colloid suspensions using enhanced molecular dynamics simulations augmented with machine learning techniques. The simulations reveal that crystallization in the model colloidal system…
We study the infinite-dimensional stochastic differential equations (ISDEs) of infinite-particle systems associated with Coulomb random point fields. The stochastic dynamics described by these ISDEs are referred to as Coulomb interacting…
We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…
Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…
We examined the Brownian motion of point defects in a two-dimensional hexagonal colloidal crystal, going beyond the conventional treatment that assumes constant diffusion coefficients. By extracting the spatially varying drift vector and…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…
Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct…
Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differential equations (SDEs) driven by the Brownian motion. However,…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…
The coarse-grained molecular dynamics (MD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the…