Presenter:	Riccardo Ben Alì Zinati
Affiliation:	USI - Università della Svizzera Italiana
Title:	Generalized Bayesian inference for chaotic systems
Authors:	Riccardo Ben Alì Zinati, Antonio di Noia, Heikki Haario and Antonietta Mira
Abstract:	Chaotic systems arise in many scientific fields, from population dynamics to atmospheric flows, and pose a fundamental challenge for statistical inference since their likelihood functions are typically either mathematically intractable or computationally prohibitive to evaluate. Moreover, infinitesimal perturbations in parameters or stochastic noise can produce markedly different trajectories, making the inverse problem of parameter recovery particularly challenging. Here, we present a simple yet general approach that circumvents explicit likelihood formulations by representing observed data and simulated outputs as point clouds in the state space. Machine learning-inspired distance metrics quantify discrepancies between these point clouds, capturing the geometry of chaotic attractors even under strong non-linearity and partial observations. By recasting this geometric mismatch in a generalized Bayesian framework, we estimate parameters solely through model simulations, offering a robust and flexible tool for systems where conventional methods fail. We validate the method on both low-dimensional systems, where chaos often manifests as strange attractors, and on high-dimensional or spatially extended systems, where it appears as evolving spatio-temporal patterns. In each case, our method accurately recovers model parameters, providing an effective framework for rigorous data assimilation in complex chaotic environments.
Last update:	06-10-2025