Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features

Abstract

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables, and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.

References in corpus (30)

• Adam: A Method for Stochastic Optimization
• Escaping free-energy minima
• Identification of slow molecular order parameters for Markov model construction
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
• Data-driven model reduction and transfer operator approximation
• Langevin equation with colored noise for constant-temperature molecular dynamics simulations
• Single-Sweep Methods for Free Energy Calculations
• Data-driven parameterization of the generalized Langevin equation
• Iterative Reconstruction of Memory Kernels
• iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes
• A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
• Recent Developments in Methods for Identifying Reaction Coordinates
• Generalized Langevin Equation with a Non-Linear Potential of Mean Force and Non-Linear Memory Friction From a Hybrid Projection Scheme
• Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
• Numerical Integration of the Extended Variable Generalized Langevin Equation with a Positive Prony Representable Memory Kernel
• Machine Learning for Prediction with Missing Dynamics
• Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics
• Likelihood-based non-Markovian models from molecular dynamics
• Exact dynamical coarse-graining without time-scale separation
• Data-driven molecular modeling with the generalized Langevin equation
• Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromolecules
• MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
• Learning Stochastic Dynamics with Statistics-Informed Neural Network
• Machine learning based non-Newtonian fluid model with molecular fidelity
• Coarse-graining Langevin dynamics using reduced-order techniques
• Machine learning memory kernels as closure for non-Markovian stochastic processes
• DeePN${}^2$: A deep learning-based non-Newtonian hydrodynamic model
• Discovery of slow variables in a class of multiscale stochastic systems via neural networks
• Optimal renormalization of multi-scale systems

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• Data-driven dynamical coarse-graining for condensed matter systems
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