Response Theory via Generative Score Modeling
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1.
Nordic Institute for Theoretical Physics
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2.
California Institute of Technology
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3.
Massachusetts Institute of Technology
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.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
The authors thank three anonymous reviewers for their suggestions which greatly enhanced the scope, quality, and presentation of the Letter. L. T. G. gratefully acknowledges support from the Swedish Research Council (Vetenskapsrådet) Grant No. 638-2013-9243. K. D. acknowledges support from Schmidt Sciences and the Cisco Foundation. A. S. and L. T. G. acknowledge support from Schmidt Sciences through the Bringing Computation to the Climate Challenge, an MIT Climate Grand Challenge Project. A. S. thanks Fabrizio Falasca and Glenn Flierl for their invaluable suggestions in improving preliminary versions of this work. T. B. acknowledges the support of the community at Livery Studio and useful discussions with Bryan Riel on generative modeling.
Data Availability
The code utilized in this work is publicly available for further study and replication: https://anonymous.4open.science/r/PrivateGenLRT-052E/generate/allen_cahn_model.jl
We used the publicly available code base T. Bischoff and K. Deck https://github.com/CliMA/CliMAgen.jl/ as the backbone for training the models.
Supplemental Material
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Additional details
- Swedish Research Council
- 638-2013-9243
- Cisco Foundation
- Accepted
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2024-11-18Accepted
- Available
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2024-12-31Published online
- Caltech groups
- Division of Engineering and Applied Science (EAS)
- Publication Status
- Published