Related papers: Coarse-Grained Dynamics with Spatial Disorder and …

In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using…

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional…

In distributed and federated learning algorithms, communication overhead is often reduced by performing multiple local updates between communication rounds. However, due to data heterogeneity across nodes and the local gradient noise within…

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of…

Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some…

The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We…

We examine coarsening of field-excitation patterns of the sine-Gordon (SG) model, in two and three spatial dimensions, identifying it as universal dynamics near non-thermal fixed points. The SG model is relevant in many different contexts,…

Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…

Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the…

This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential…

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

Coarse-grained (CG) force field methods for molecular systems are a crucial tool to simulate large biological macromolecules and are therefore essential for characterisations of biomolecular systems. While state-of-the-art deep learning…

Lagrangian Coherent Structures (LCS) are flow features which are defined to objectively characterize complex fluid behavior over a finite time regardless of the orientation of the observer. Fluidic applications of LCS include geophysical,…

A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.The schemes are based on a weak formulation of a…

Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective…

Gradient-domain machine learning (GDML) is an accurate and efficient approach to learn a molecular potential and associated force field based on the kernel ridge regression algorithm. Here, we demonstrate its application to learn an…