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

arXiv: https://arxiv.org/abs/2606.24966 · HTML: https://mlsanity.com/paper/2606.24966/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [From system models to class models: An in-context learning paradigm](https://mlsanity.com/paper/2308.13380/) (2023)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Fine Tuning a Simulation-Driven Estimator](https://mlsanity.com/paper/2504.04480/) (2025)

## Abstract (arXiv)

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.