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Response Theory via Generative Score Modeling
Open accessPublished version of a preprint
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. 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. Published by the American Physical Society 2024
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Metadata
- Authors
- Giorgini, L. T., Deck, K., Bischoff, T., & Souza, A.
- Affiliations
- Nordic Institute for Theoretical Physics (SE)
- California Institute of Technology (US)
- Independent Researcher
- Massachusetts Institute of Technology (US)
- Corresponding author
- Giorgini, Ludovico Theo
- Deck, Katherine
- Bischoff, Tobias
- Souza, Andre
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2024-12-31
- Volume
- 133
- Issue
- 26
- Pages
- 267302-267302
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W4405943563
- Cited by
- 13
- References
- 4
- Citations by year
- 2026: 7 · 2025: 6
- FWCI
- 1.90
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- Vetenskapsrådet (638-2013-9243)
- Cisco Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- response theory, dynamical systems, external disturbances, non-Gaussian statistics, stochastic partial differential equations, Ornstein-Uhlenbeck process, stochastic Allen-Cahn equation, Navier-Stokes equations, spatially correlated noise
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