Collaborative Research: MATH-DT Closing the generalization gap of digital twins

From the weather to human health to fighter jets, there are many complex systems whose outcomes we would like to predict and control. To achieve these goals, scientists and engineers often build digital twins---computer models that emulate and interact with the underlying physical systems. The current project describes fundamental research into the generalization ability of digital twins: to what degree can digital twins predict outcomes under conditions they have not previously encountered? For example, if the digital twin for an airplane has only seen data collected under normal operating conditions, can it accurately predict the plane's response to turbulence? By combining mathematical tools from nonlinear dynamics and computational tools from machine learning, this project aims to develop fundamental theories on generalization and build robust digital twins that can perform well in extreme or unexpected conditions. While the proposed framework applies to a broad class of complex systems, it is first being applied to circadian rhythms, which are the internal timekeeping mechanisms of the human body. Human biological clocks are increasingly subject to disturbances introduced by modern lifestyles such as long-haul air travel and nighttime computer use. Predictive digital twins can give personalized recommendations on effective interventions, such as optimal strategies to speed up recovery from jet lags. The project will also provide opportunities to teach modern mathematical concepts to a diverse population of undergraduate and graduate students. Through this project, students learn valuable skills in mathematical modeling, data analysis, science communication, and gain first-hand experience in building and managing state-of-the-art machine learning pipelines. Current domain-agnostic digital twins based on deep neural networks are very expressive but can struggle when generalizing beyond their training conditions. Physics-based digital twins, on the other hand, generalize better to unseen conditions thanks to the strong inductive bias built into the model. On the other hand, they are often not sufficiently flexible to fully capture the rich dynamics in data. This project develops a new class of hybrid digital twins with tunable physics-based and domain-agnostic components, allowing practitioners to balance expressivity versus generalization, depending on the available data and the nature of the task. Utilizing concepts such as basins of attraction in multistable dynamical systems, a key objective of the project is to quantify how the generalization ability of the digital twin changes as the weights assigned to the two components are adjusted. In particular, the project explores the possibility that a properly weighted domain-agnostic component in the hybrid digital twin can sometimes improve out-of-distribution generalization, especially when the inductive bias provided by the physics-based component is imperfect. Digital twins that generalize to unseen conditions are crucial to applications such as finding optimal interventions for restoring disrupted circadian rhythms. For example, to find optimal strategies to speed up recovery from jet lags, a digital twin needs to predict the dynamics of a severely perturbed circadian clock based on data gathered mostly from normally operating clocks. These investigations will guide the creation of more robust digital twins and help inform critical decisions under new or uncertain conditions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.