Statistical Parameter Calibration via the Generalized Fluctuation Dissipation Theorem and Generative Modeling
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| Format: | Preprint |
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2025
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| author | Giorgini, Ludovico T. Bischoff, Tobias Souza, Andre N. |
| author_facet | Giorgini, Ludovico T. Bischoff, Tobias Souza, Andre N. |
| contents | We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with respect to drift and diffusion parameters admits an exact linear-response representation as a time-correlation integral evaluated along unperturbed dynamics alone, without perturbed simulations, adjoint derivations, or tangent-linear models. The key idea is to interpret infinitesimal parameter variations as causal perturbations of the dynamics, thereby bringing the Generalized Fluctuation-Dissipation Theorem to inverse problems. The resulting kernels couple observables to the score of the invariant density, for which modern score-estimation methods provide practical non-Gaussian estimators. We validate the framework across a hierarchy of models, from analytically tractable processes to stochastic parameterization in the chaotic Lorenz-96 system, and show that a single baseline trajectory can recover parameter sensitivities and calibration updates with accuracy comparable to finite-difference approaches. More broadly, the framework opens a new route to model calibration, statistical inverse problems, and uncertainty quantification when the quantities of interest are long-time statistics of complex dynamical systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical Parameter Calibration via the Generalized Fluctuation Dissipation Theorem and Generative Modeling Giorgini, Ludovico T. Bischoff, Tobias Souza, Andre N. Chaotic Dynamics We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with respect to drift and diffusion parameters admits an exact linear-response representation as a time-correlation integral evaluated along unperturbed dynamics alone, without perturbed simulations, adjoint derivations, or tangent-linear models. The key idea is to interpret infinitesimal parameter variations as causal perturbations of the dynamics, thereby bringing the Generalized Fluctuation-Dissipation Theorem to inverse problems. The resulting kernels couple observables to the score of the invariant density, for which modern score-estimation methods provide practical non-Gaussian estimators. We validate the framework across a hierarchy of models, from analytically tractable processes to stochastic parameterization in the chaotic Lorenz-96 system, and show that a single baseline trajectory can recover parameter sensitivities and calibration updates with accuracy comparable to finite-difference approaches. More broadly, the framework opens a new route to model calibration, statistical inverse problems, and uncertainty quantification when the quantities of interest are long-time statistics of complex dynamical systems. |
| title | Statistical Parameter Calibration via the Generalized Fluctuation Dissipation Theorem and Generative Modeling |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2509.19660 |