Physics-informed Learning for Dynamical Systems from Scarce Data

This award will support research that aims to develop trustworthy artificial intelligence functionality for systems with a physical embodiment, e.g., robots, unmanned vehicles, and infrastructure networks. While modern learning-based techniques offer unprecedented capabilities for nonlinear modeling and control, they often rely on excessive amounts of data and computing power and fail to meet safety specifications.

This research will develop a new breed of learning techniques that effectively leverage existing knowledge, such as that based on the laws of physics. The resulting techniques have the potential to help safely deploy learning-enabled functionality with reasonable data requirements and calculated risks in nominal and off-nominal situations. Therefore, the research will help create an advantage for the U.S. in developing artificial intelligence while informing the public about the inherent risks.

This research will bridge several disciplines including dynamical systems, control theory, deep learning, optimization, and applied mathematics. The award will support the training of students from diverse backgrounds and equip them with a mindset of inclusion necessary to counter the increasingly interdisciplinary challenges society is facing.

Learning-based techniques offer new capabilities to model unknown dynamical systems and, in turn, facilitate predictions of future values of interest, synthesize control strategies, and verify safety of the closed-loop system. On the other hand, when employed for dynamical systems with a physical embodiment, purely data-driven methods can result in poor data efficiency, fail to generalize beyond their mere training domain, and even violate the underlying laws of physics.

These deficiencies become particularly emphasized when the training dataset is relatively small. The central thesis of this project is that the effective inclusion of a-priori knowledge into learning can significantly improve data efficiency and model generalization to previously unseen regions of the state space. It focuses on physics-informed learning in two settings with severe data scarcity: The first is on learning after an abrupt change in the dynamics during operation where learning is limited by data available essentially from a single trajectory.

The second is on training deep neural networks for dynamical systems using a “handful” of system trajectories, matching, or exceeding, the accuracy of conventional, merely data-driven deep learning methods with multiple orders of magnitude fewer trajectories. While the suitable learning artifacts, and the expectations from learning, are different in these two settings, the type of, and means for incorporating physics-based knowledge into learning are based on similar principles.

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.