Physics and causally constrained discrete-time neural models of turbulent dynamical systems

TL;DR

This paper introduces a physics-informed neural modeling framework for turbulent systems that enforces energy conservation and causality, accurately capturing system statistics and responses.

Contribution

It develops a novel neural modeling approach incorporating physical and causal constraints for turbulent dynamical systems from data.

Findings

Models accurately reproduce stationary statistics.

Framework works on stochastic Charney-DeVore and Lorenz-96 systems.

Suppresses spurious interactions across degrees of freedom.

Abstract

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of temporally discrete trajectories. We then impose causal constraints to suppress spurious interactions across degrees of freedom. The resulting neural models accurately capture stationary statistics and responses to both small and large external forcings. We demonstrate the framework on the stochastic Charney-DeVore equations and on a symmetry-broken Lorenz-96 system. The framework is broadly applicable to reduced-order modeling of turbulent dynamical systems from observational data.