Related papers: Data-driven Efficient Solvers for Langevin Dynamic…
Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
Particle-laden flows are simulated at various scales using numerical techniques that range from particle-resolved Direct Numerical Simulations (pr-DNS) for small-scale systems to Lagrange point-particle methods for laboratory-scale…
We establish a general Langevin Dynamics model of interacting, single-domain magnetic nanoparticles in liquid suspension at finite temperature. The model couples the LLG equation for the moment dynamics with the mechanical rotation and…
Despite rapid improvements in the performance of central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks…
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…
Traditional computational fluid dynamics and physics-informed neural networks (PINNs) often suffer from high computational cost, mesh sensitivity, and reduced accuracy for strongly nonlinear and time-dependent flows. To address these…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
We apply well-established concepts of Langevin sampling to derive a new class of algorithms for the efficient computation of free energy differences of fluctuating particles embedded in a 'fast' membrane, i.e., a membrane that…
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
This paper is concerned with collective variables, or reaction coordinates, that map a discrete-in-time Markov process $X_n$ in $\mathbb{R}^d$ to a (much) smaller dimension $k \ll d$. We define the effective dynamics under a given…
Chemical reactions in multidimensional driven systems are typically described by a time-dependent rank-1 saddle associated with one reaction and several orthogonal coordinates (including the solvent bath). To investigate reactions in such…
For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker-Planck dynamics involving an arbitrary force $F(x)$ and an arbitrary diffusion coefficient $D(x)$,…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
Stochastic Langevin dynamics has been traditionally used as a tool to describe non-equilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their…
Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed…
The recently discovered supersymmetric generalizations of Langevin dynamics and Kramers equation can be utilized for the exploration of free energy landscapes of systems whose large time-scale separation hampers the usefulness of standard…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…