Data-driven modeling of multiscale phenomena with applications to fluid turbulence

TL;DR

This paper presents a data-driven framework for creating accurate, general equivariant models of multiscale phenomena, demonstrated through fluid turbulence to effectively capture small-scale effects like backscatter.

Contribution

The paper introduces a physics-agnostic, data-driven modeling approach for multiscale systems, successfully applied to fluid turbulence to model small-scale influences.

Findings

Effective modeling of small-scale effects including backscatter.

Accurate and general equivariant models without relying on specific physics assumptions.

Demonstrated success in two-dimensional turbulence simulations.

Abstract

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated using incompressible fluid turbulence as an example that is representative, practically important, reasonably simple, and exceedingly well studied. We use direct numerical simulations of freely decaying turbulence in two spatial dimensions to infer an effective field theory comprising explicit, interpretable evolution equations for both the large (resolved) and small (modeled) scales. The resulting closed system of equations is capable of accurately describing the effect of small scales, including backscatter -- the flow of energy from small to large scales, which is particularly pronounced in two dimensions -- which is an outstanding challenge that, to our knowledge, no existing alternative successfully tackles.