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.

翻译：随着柔性物体在许多应用（例如软体机器人）中的日益普及，对其动力学建模已成为该领域的新兴课题。由于柔性材料的特性，软体物体的运动通常具有高度非线性，因此难以预测。数据驱动方法似乎有望对这些复杂动力学进行建模，但往往忽略了基本的物理原理，从而导致其不可靠且泛化能力有限。为解决这一问题，我们提出了一种物理约束学习方法，该方法结合了强大的学习工具与可靠的物理模型。我们的方法利用从观测中收集的数据，将其输入一个由分布式端口-哈密顿模型进行物理约束的高斯过程。基于高斯过程的贝叶斯特性，我们不仅能够学习系统的动力学，还能实现不确定性量化。此外，所提出的方法保留了端口-哈密顿系统的组合特性。