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Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We study the effect of confinement on diffusion limited bimolecular reactions within a lattice model where a small number of reactants diffuse amongst a much larger number of inert particles. When the number of inert particles is held…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
In Moln\'ar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle…
A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local…
We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved…
Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used…
We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases,…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to directly learn the…
As robots venture into the real world, they are subject to unmodeled dynamics and disturbances. Traditional model-based control approaches have been proven successful in relatively static and known operating environments. However, when an…
We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous…
Lattice Boltzmann models provide better understanding with mesoscopic eyesight on multi-component diffusion than macroscopic models. Based on the kinetic theory and starting from the He-Luo model, the state-of-the-art multi-component…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
Prior distributions of binarized natural images are learned by using a Boltzmann machine. According the results of this study, there emerges a structure with two sublattices in the interactions, and the nearest-neighbor and…
We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighbouring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting…