Data-driven dynamical systems discovery: Embracing uncertainty.

Building models for biological, chemical, and physical systems has traditionally relied on domain-specific intuition about which interactions and features most strongly influence a system. Our group balances traditional modeling with data-driven methods from machine learning, statistics, and optimization to semi-automate model construction to generate new scientific hypotheses and engineer systems. In particular, we have developed sparse-model selection methods to identify ODEs from time-series data when not all dynamic states of the system are measured, leading to inherent unidentifiability in the model structure. By studying the structure of the underlying symmetries that lead to unidentifiability, we find several implications for parsimonious model discovery in terms of how the functional forms of the feature library impact the ease of computation and the interpretability of the discovered models. Additionally, we explore the impacts of poor data sampling and quality on the model recovery when all dynamic states are measured, demonstrating that standard orthogonal polynomial libraries do not resolve the problem of poor conditioning and suggesting that more uncertainty-robust methods are needed.