Data-driven parameterization of the generalized Langevin equation

Abstract

We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.

References in corpus (3)

• Colored-noise thermostats à la carte
• The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics
• Parametric Reduced Models for the Nonlinear Schrödinger Equation

Cited by in corpus (45)

• iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes
• Coarse-Grained Modelling Out of Equilibrium
• Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
• Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models
• Likelihood-based non-Markovian models from molecular dynamics
• Data-driven molecular modeling with the generalized Langevin equation
• Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systems
• Learning Stochastic Dynamics with Statistics-Informed Neural Network
• Machine learning based non-Newtonian fluid model with molecular fidelity
• On the estimation of the Mori-Zwanzig memory integral
• Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
• Ab Initio Generalized Langevin Equation
• Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
• Coarse-graining Langevin dynamics using reduced-order techniques
• Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features
• Resampling with neural networks for stochastic parameterization in multiscale systems
• Systematic derivation of hybrid coarse-grained models
• Machine learning memory kernels as closure for non-Markovian stochastic processes
• Data-driven model reduction for stochastic Burgers equations
• Generalized Langevin equations for systems with local interactions
• Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion
• Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework
• From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics
• Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel
• Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids
• Statistical Inference of 1D Persistent Nonlinear Time Series and Application to Predictions
• Non-Markovian systems out of equilibrium: Exact results for two routes of coarse graining
• DeePN${}^2$: A deep learning-based non-Newtonian hydrodynamic model
• On the Generalised Langevin Equation for Simulated Annealing
• On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-dimensional lattice model
• Oscillating states of periodically driven anharmonic Langevin systems
• Memory-based reduced modelling and data-based estimation of opinion spreading
• Optimal renormalization of multi-scale systems
• Generalized second fluctuation-dissipation theorem in the nonequilibrium steady state: Theory and applications
• Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations
• Analytical and Computational Studies of Correlations of Hydrodynamic Fluctuations in Shear Flow
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction
• Effective Mori-Zwanzig equation for the reduced-order modeling of stochastic systems
• Renormalization and blow-up for the 3D Euler equations
• Faber approximation to the Mori-Zwanzig equation
• Inchworm Monte Carlo method for open quantum systems
• The Interplay between Memory and Potentials of Mean Force: A Discussion on the Structure of Equations of Motion for Coarse Grained Observables
• Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force
• Linear Response Based Parameter Estimation in the Presence of Model Error
• NySALT: Nyström-type inference-based schemes adaptive to large time-stepping