Hierarchical Bayesian Model Learns Dynamical Systems from Sparse Data

Estimating parameters for dynamical systems often presents a significant challenge, particularly when dealing with data that is sparse, noisy, and irregularly sampled, leading to ill-conditioned problems. However, when multiple related datasets are available, they can provide crucial additional information if their shared underlying structure and individual variability are effectively modeled. This research proposes a novel solution to this problem. The study introduces a hierarchical Bayesian framework designed for probabilistic meta-learning within dynamical systems. This framework models dataset-specific parameters as if they are drawn from a common, shared population distribution, allowing the model to leverage information across datasets. By embedding a numerical Ordinary Differential Equation (ODE) solver within a gradient-based Markov Chain Monte Carlo (MCMC) process, the approach facilitates efficient posterior inference for both the shared population and individual dataset-specific parameter distributions. Experimental results demonstrate that this method significantly improves predictive performance compared to unpooled methods, highlighting its potential for data-efficient system identification in scenarios with limited data.