Parametric perturbations and varying initial conditions are among the most common types of uncertainties found in dynamical system models. This problem has been studied from a frequency-domain perspective in depth. But these methods are not easily applicable in all scenarios, especially ones where time-domain, real-time implementations are needed. Towards that end, in this project, we explore alternative approaches to quantify the robustness of dynamical system models to parametric uncertainties.
Methods: We will explore sensitivity-based and differentiably quantifable metrics to define robustness to system parameters and uncertain initial conditions. Possible dynamical system examples include: ODE models, neural ODEs of neural networks, graph models, and more. Application examples include: synthetic biology, classification problems using neural networks, adaptive cruise control, and more. The overarching goal is to guide modelers and application engineers with tolerable levels of parametric uncertainty and pave the way for new cost functions in data-driven estimation and control.
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