Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling

• URL: http://arxiv.org/abs/2504.13333v1
• Date: Thu, 17 Apr 2025 20:54:33 GMT
• Title: Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling
• Authors: Ludovico T. Giorgini, Fabrizio Falasca, Andre N. Souza,
• Abstract summary: We present a novel data-driven framework for estimating the response of higher-order moments of nonlinear systems to small external perturbations.<n>Standard implementations rely on Gaussian approximations, which can often accurately predict the mean response but usually introduce significant biases in higher-order moments.<n>We combine GFDT with recent advances in score-basedgenerative modeling, which enable direct estimation of the score function without requiring full density reconstruction.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation-Dissipation Theorem (GFDT) links the unperturbed steady-state distribution to the system's linear response. Standard implementations rely on Gaussian approximations, which can often accurately predict the mean response but usually introduce significant biases in higher-order moments, such as variance, skewness, and kurtosis. To address this limitation, we combine GFDT with recent advances in score-based generative modeling, which enable direct estimation of the score function from data without requiring full density reconstruction. Our method is validated on three reduced-order stochastic models relevant to climate dynamics: a scalar stochastic model for low-frequency climate variability, a slow-fast triad model mimicking key features of the El Nino-Southern Oscillation (ENSO), and a six-dimensional stochastic barotropic model capturing atmospheric regime transitions. In all cases, the approach captures strongly nonlinear and non-Gaussian features of the system's response, outperforming traditional Gaussian approximations.

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