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arXiv · 2606.24966

Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach

Cristian Brugnara·Lea Multerer·Marco Forgione·Laura Azzimonti
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Abstract

Estimating parameters of dynamical systems from sparse, noisy, and irregularly sampled data is often severely ill-conditioned. When multiple related datasets are available, they provide additional information if the shared structure and variability are properly modeled. We propose a hierarchical Bayesian framework for probabilistic meta-learning in dynamical systems, modeling dataset-specific parameters as draws from a shared population distribution. A numerical ODE solver is embedded within gradient-based MCMC to enable efficient posterior inference of the shared population and dataset-specific parameter distribution. Experiments show improved predictive performance over unpooled methods, highlighting the potential for data-efficient system identification in settings with sparse data.

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Cristian Brugnara, Lea Multerer, Marco Forgione, Laura Azzimonti. 2026-06-23. Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach. https://arxiv.org/abs/2606.24966

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