Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

建议了一种物理约束学习方法，将强大的学习工具与可靠的物理模型相结合，通过高斯过程对观测到的数据进行处理，并将分布式Port-Hamiltonian模型与其物理约束相关联，以学习系统的动力学，并进行不确定性量化，并且保留了Port-Hamiltonian系统的组合性质。

物理约束学习带不确定性的PDE系统的Port-Hamiltonian模型