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A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better…
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded…
The phenomena of diffusion in multicomponent (more than two components) mixtures are very universal in both science and engineering, and from mathematical point of view, they are usually described by the Maxwell-Stefan (MS) based continuum…
A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive…
Decomposing knowledge into interchangeable pieces promises a generalization advantage when there are changes in distribution. A learning agent interacting with its environment is likely to be faced with situations requiring novel…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
We consider distributed multitask learning problems over a network of agents where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize.…
We present a highly efficient lattice Boltzmann (LB) kinetic model for thermal liquid-vapor system. Three key components are as beow: (i) a discrete velocity model by Kataoka \emph{et al.} [Phys. Rev. E \textbf{69}, 035701(R)(2004)]; (ii) a…
One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…
We develop diffusion models for lattice gauge theories which build on the concept of stochastic quantization. This framework is applied to $U(1)$ gauge theory in $1+1$ dimensions. We show that a model trained at one small inverse coupling…
We propose a data-driven approach using a Restricted Boltzmann Machine (RBM) to solve the Schr\"odinger equation in configuration space. Traditional Configuration Interaction (CI) methods construct the wavefunction as a linear combination…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
This paper addresses the problem of learning reaction-diffusion (RD) systems from data while ensuring physical consistency and well-posedness of the learned models. Building on a regularization-based framework for structured model learning,…
Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric…
We study the collapse and revival of interference patterns in the momentum distribution of atoms in optical lattices, using a projection technique to properly account for the fixed total number of atoms in the system. We consider the common…