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In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

Based on the characteristics of the multi-scale and similarity at different scales in turbulent flow, we propose a scale decomposition for solving the turbulence problem of incompressible Newtonian fluid. The solution domain is decomposed…

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

We consider a class of smooth $N$-player noncooperative games, where player objectives are expectation-valued and potentially nonconvex. In such a setting, we consider the largely open question of efficiently computing a suitably defined…

Stochastic partial differential equations (SPDEs) describe the evolution of random processes over space and time, but their solutions are often analytically intractable and computationally expensive to estimate. In this paper, we propose…

The nested Extremum Seeking (nES) algorithm is a model-free optimization method that has been shown to converge to a neighborhood of a Nash equilibrium. In this work, we demonstrate that the same nES dynamics can instead be made to converge…

Applications of combinatorial auctions (CA) as market mechanisms are prevalent in practice, yet their Bayesian Nash equilibria (BNE) remain poorly understood. Analytical solutions are known only for a few cases where the problem can be…

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to…

We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions…

In this paper a reaction-diffusion type equation is the starting point for setting up a genuine thermodynamic reduction, i.e. involving a finite number of parameters or collective variables, of the initial system. This program is carried…

We discuss applications of statistical-mechanical lattice-gas models to study static and dynamic aspects of electrochemical adsorption. The strategy developed to describe specific systems includes microscopic model formulation, calculation…

We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

It has been reported recently that the equipartition theorem is violated in molecular dynamics simulations with periodic boundary condition [Shirts et al, J. Chem. Phys. 125, 164102 (2006)]. This effect is associated with the conservation…

We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating model explicitly into consideration. Our approach treats the…

equilibrium-c (eqc) is a program for computing the composition of gas mixtures in chemical equilibrium. In typical usage, the program is given a known thermodynamic state, such as fixed temperature and pressure, as well as an initial…

This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…

Neural networks inspired by differential equations have proliferated for the past several years. Neural ordinary differential equations (NODEs) and neural controlled differential equations (NCDEs) are two representative examples of them. In…