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

• URL: http://arxiv.org/abs/2606.24966v1
• Date: Tue, 23 Jun 2026 09:41:25 GMT
• Title: Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach
• Abstract summary: We propose a hierarchical Bayesian framework for probabilistic meta-learning in dynamical systems.<n>A numerical ODE solver is embedded within gradient-based MCMC to enable efficient posterior inference of the shared population and dataset-specific parameter distribution.<n>Experiments show improved predictive performance over unpooled methods, highlighting the potential for data-efficient system identification in settings with sparse data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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