Accurate models of mechanical system dynamics are often critical for
model-based control and reinforcement learning. Fully data-driven dynamics
models promise to ease the process of modeling and analysis, but require
considerable amounts of data for training and often do not generalize well to
unseen parts of the state space. Combining data-driven modelling with prior
analytical knowledge is an attractive alternative as the inclusion of
structural knowledge into a regression model improves the model's data
efficiency and physical integrity. In this article, we survey supervised
regression models that combine rigid-body mechanics with data-driven modelling
techniques. We analyze the different latent functions (such as kinetic energy
or dissipative forces) and operators (such as differential operators and
projection matrices) underlying common descriptions of rigid-body mechanics.
Based on this analysis, we provide a unified view on the combination of
data-driven regression models, such as neural networks and Gaussian processes,
with analytical model priors. Further, we review and discuss key techniques for
designing structured models such as automatic differentiation.

本文综述了一些通过将数据驱动建模与先前的解析知识相结合的监督回归模型，以在具有刚体力学描述的系统动力学建模中提高数据的效率和物理完整性，并分析了刚体力学的各种潜在函数和算子。