Physics-informed Learning for Dynamical Systems from Scarce Data

该奖项将支持旨在为具有物理体现的系统（如机器人、无人驾驶车辆和基础设施网络）开发可信赖的人工智能功能的研究。虽然现代基于学习的技术为非线性建模和控制提供了前所未有的能力，但它们往往依赖于过多的数据和计算能力，无法满足安全规范。这项研究将开发一种新的学习技术，有效地利用现有的知识，如基于物理定律的知识。由此产生的技术有可能帮助在名义和非名义情况下，以合理的数据需求和计算的风险安全地部署支持学习的功能。因此，这项研究将有助于为美国在发展人工智能方面创造优势，同时向公众通报其固有的风险。这项研究将跨越多个学科，包括动力系统、控制理论、深度学习、优化和应用数学。该奖项将支持培养来自不同背景的学生，并使他们具备必要的包容心态，以应对社会面临的日益跨学科的挑战。基于学习的技术提供了新的能力来建模未知的动态系统，反过来，促进对未来感兴趣的值的预测，综合控制策略，并验证闭环系统的安全性。另一方面，当用于具有物理体现的动力系统时，纯粹的数据驱动方法可能导致数据效率低下，无法推广到其单纯的训练领域之外，甚至违反物理的基本定律。当训练数据集相对较小时，这些缺陷变得特别突出。该项目的中心论点是，有效地将先验知识纳入学习可以显着提高数据效率和模型泛化到以前未见过的状态空间区域。它侧重于在两种数据严重缺乏的情况下的物理知识学习：第一种是在操作过程中动态突然变化之后的学习，其中学习基本上受到来自单一轨迹的可用数据的限制。第二个是使用“少数”系统轨迹来训练动态系统的深度神经网络，匹配或超过传统的，仅仅是数据驱动的深度学习方法的精度，轨迹要少几个数量级。虽然在这两种情况下，合适的学习产物和学习的期望是不同的，但将基于物理的知识纳入学习的类型和方法是基于类似的原则。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.