Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes
This work addresses data efficiency and constraint adherence in learning dynamics for mechanical systems, representing an incremental improvement in domain-specific modeling.
The paper tackled the challenge of identifying constrained dynamics in mechanical systems by combining analytical mechanics with Gaussian process regression to improve data efficiency and ensure constraint integrity, resulting in a model that adheres to Gauss' principle and enables inference of unconstrained accelerations and knowledge transfer between constraint configurations.
The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model's data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere to Gauss' principle of least constraint. In return, predictions of the system's acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.