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We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike…
This paper formulates two 3D stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. The two models have two distinct noise sources. One is general noise whereas the other is…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
Electron beam-induced current (EBIC) imaging in the scanning transmission electron microscope (STEM), STEM-EBIC, provides direct access to carrier transport at the nanoscale. While well established in bulk SEM geometries, its application to…
Molecular dynamics simulations are a powerful tool to study diffusion processes in battery electrolyte and electrode materials. From a single molecular dynamics simulation many properties relevant to diffusion can be obtained, including the…
We propose two metadynamics (MetaD)-based methodologies for efficiently mapping free energy surfaces (FESs) of multiple interacting carriers diffusing in crystalline solids. Our approaches circumvent the challenges of high-dimensional…
In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…
Despite the growing level of technological advancement that characterizes extrusion-deposition additive manufacturing technology, there remains a significant knowledge gap in fully understanding the process-structure-property relationship…
This paper investigates in hatching process strategies for additive manufacturing using an electron beam by numerical simulations. The underlying physical model and the corresponding three dimensional thermal free surface lattice Boltzmann…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we investigate the influence of step edge diffusion (SED) and evaporation on Molecular Beam Epitaxy (MBE). Based on these investigations we propose two strategies to optimize…
In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical-systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic…
Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful…
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the…
Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter…
In this paper, we introduce and evaluate a data-driven staged mixture modeling technique for building density, regression, and classification models. Our basic approach is to sequentially add components to a finite mixture model using the…
Developing tailored semiconductor heterostructures on demand represents a critical capability for addressing the escalating performance demands in electronic and optoelectronic devices. However, traditional fabrication methods remain…