Learning Dynamical Systems from Multiple Sparse Datasets: A Hierarchical Bayesian Modeling Approach
It addresses the ill-conditioned problem of estimating dynamical system parameters from sparse data by leveraging shared structure across related datasets, enabling more data-efficient system identification.
The paper proposes a hierarchical Bayesian framework for learning dynamical systems from multiple sparse, noisy datasets, achieving improved predictive performance over unpooled methods.
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.