A General Framework for Linking Free and Forced Fluctuations via Koopmanism

TL;DR

This paper introduces a Koopman operator-based framework to connect free and forced fluctuations in nonequilibrium systems, enabling interpretable response analysis and coarse-graining, demonstrated on a stochastic Lorenz model.

Contribution

It develops a generalized fluctuation-dissipation framework using Koopman operators, allowing for data-driven and coarse-grained analysis of system responses.

Findings

Koopman-based response operators are interpretable and sum of decaying modes.

The approach works effectively on a stochastic Lorenz '63 model.

Supports development of equation-agnostic, data-driven response methods.

Abstract

The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to deliver an intepretable form of the response operators written as a sum of exponentially decaying terms, each associated one-to-one with a mode of natural variability of the system. Here we showcase on a stochastically forced version of the celebrated Lorenz '63 model the feasibility and skill of such an approach by considering different Koopman dictionaries, which allows us to treat also seamlessly coarse-graining approaches like the Ulam method. Our findings provide support for the development of response theory-based investigation methods also in an equation-agnostic, data-driven environment.