{"id":3223,"date":"2025-04-21T07:02:29","date_gmt":"2025-04-21T07:02:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/04\/21\/2504-13333\/"},"modified":"2025-04-21T07:02:29","modified_gmt":"2025-04-21T07:02:29","slug":"2504-13333","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/04\/21\/2504-13333\/","title":{"rendered":"Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling"},"content":{"rendered":"

Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling
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arXiv:2504.13333v1 Announce Type: new
\nAbstract: 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.<\/div>\n

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\n Ludovico T. Giorgini, Fabrizio Falasca, Andre N. Souza
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Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling arXiv:2504.13333v1 Announce Type: new 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. […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,2051,112],"tags":[2411,1957,606],"class_list":["post-3223","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-nlin-cd","category-stat-ml","tag-fluctuation","tag-response","tag-stochastic"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3223"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=3223"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/3223\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=3223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=3223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=3223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}