Departmental Colloquium

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.

The ability of a system to correctly respond to sudden adversity is critical for high-level autonomy in complex, novel, or remote environments. By assuming continuing structural knowledge about the system, classical methods of adaptive or robust control largely attempt to design control laws which enable the system to complete its original task even after an adverse event. However, catastrophic events such as physical system damage may render the original task impossible to complete. In other words, any control law that attempts to complete the task is doomed to fail. Instead, a high-level planner should understand which tasks can be certifiably completed given the current knowledge, and then formulate appropriate control laws. To this end, in this talk I will present an emergent twin effort of design-time resilience and mission-time guaranteed performance. Combining methods of reachability analysis, optimal control, and switched systems, these approaches compute a set of certifiably completable tasks consistent with the planner’s partial knowledge, estimate the time and resources necessary to complete them, and synthesize appropriate long-term plans and low-level control laws using online learning and adaptation. In describing this framework, this talk will briefly present several applications to autonomous vehicles across domains, identifying promising future directions of research such as resilience of high-level tasks, reachability with safety and state constraints, and data-driven incremental certification.

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