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

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.

Fabrizio Falasca

Postdoctoral researcher [he/him]

Laure Zanna

Joseph B. Keller and Herbert B. Keller Professor in Applied Mathematics; Professor of Mathematics and Data Science

My research interests include Climate Dynamics, Physical Oceanography, Applied Math, Numerical Methods, and Data Science.