Phys Rev Lett. 2024 Dec 31;133(26):267302. doi: 10.1103/PhysRevLett.133.267302.
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.
PMID:39879063 | DOI:10.1103/PhysRevLett.133.267302
