Response Theory via Generative Score Modeling

Ludovico Theo Giorgini; Katherine Deck; Tobias Bischoff; Andre Souza

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arXiv · 2402.01029

Response Theory via Generative Score Modeling

Ludovico Theo Giorgini·Katherine Deck·Tobias Bischoff·Andre Souza

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Abstract

We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics. We numerically validate our approach using time-series data from three different stochastic partial differential equations of increasing complexity: an Ornstein-Uhlenbeck process with spatially correlated noise, a modified stochastic Allen-Cahn equation, and the 2D Navier-Stokes equations. We demonstrate the improved accuracy of the methodology over conventional methods and discuss its potential as a versatile tool for predicting the statistical behavior of complex dynamical systems.

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Ludovico Theo Giorgini, Katherine Deck, Tobias Bischoff, Andre Souza. 2024-02-01. Response Theory via Generative Score Modeling. https://arxiv.org/abs/2402.01029

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