Related papers: Computational statistical physics and hypocoercivi…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…
The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…
We address the problem of constructing accurate mathematical models of the dynamics of complex systems projected on a collective variable. To this aim we introduce a conceptually simple yet effective algorithm for estimating the parameters…
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Integrated Computational Materials Engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However,…
Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…
Chemical signaling is one of the ubiquitous mechanisms by which inter-cellular communication takes place at the microscopic level, particularly via chemotaxis. Such multi-cellular systems are popularly studied using continuum, mean-field…
It has long been recognized that the dynamics of linear quantum systems is classical in the Wigner representation. Yet many conceptually important linear problems are typically analyzed using such generally applicable techniques as…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce…