Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling predictions of their temporal evolution and analyses of thermodynamic quantities, including absorbed heat, work done on the system, and entropy production. However, inferring the Langevin equation from observed trajectories remains challenging, particularly for nonlinear and high-dimensional systems. In this study, we present a comprehensive framework that employs Bayesian …

bayesian climate cond-mat.soft cond-mat.stat-mech cs.lg diverse domains dynamics enabling equation evolution heat molecular dynamics networks neural networks physics.bio-ph predictions processes stochastic studying systems temporal uncertainty via work