Response Theory via Generative Score Modeling
- URL: http://arxiv.org/abs/2402.01029v1
- Date: Thu, 1 Feb 2024 21:38:10 GMT
- Title: Response Theory via Generative Score Modeling
- Authors: Ludovico Theo Giorgini, Katherine Deck, Tobias Bischoff, Andre Souza,
- Abstract summary: We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Fluctuation-Dissipation Theorem (FDT)
We numerically validate our approach using time-series data from a partial differential equation where the score function is available analytically.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Fluctuation-Dissipation Theorem (FDT). The methodology enables accurate estimation of system responses, especially for systems with non-Gaussian statistics, often encountered in dynamical systems far from equilibrium. Such cases often present limitations for conventional approximate methods. We numerically validate our approach using time-series data from a stochastic partial differential equation where the score function is available analytically. Furthermore, we demonstrate the improved accuracy of our methodology over conventional methods and its potential as a versatile tool for understanding complex dynamical systems. Applications span disciplines from climate science and finance to neuroscience.
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