Deep learning has achieved astonishing results on many tasks with large
amounts of data and generalization within the proximity of training data. For
many important real-world applications, these requirements are unfeasible and
additional prior knowledge on the task domain is required to overcome the
resulting problems. In particular, learning physics models for model-based
control requires robust extrapolation from fewer samples - often collected
online in real-time - and model errors may lead to drastic damages of the
system. Directly incorporating physical insight has enabled us to obtain a
novel deep model learning approach that extrapolates well while requiring fewer
samples. As a first example, we propose Deep Lagrangian Networks (DeLaN) as a
deep network structure upon which Lagrangian Mechanics have been imposed. DeLaN
can learn the equations of motion of a mechanical system (i.e., system
dynamics) with a deep network efficiently while ensuring physical plausibility.
The resulting DeLaN network performs very well at robot tracking control. The
proposed method did not only outperform previous model learning approaches at
learning speed but exhibits substantially improved and more robust
extrapolation to novel trajectories and learns online in real-time

使用理论物理知识，以很少的数据为样本，提出了一种新的深度学习方法 Deep Lagrangian Networks (DeLaN)，可用于机器人轨迹跟踪控制，能够在实时学习中更快速，更准确地进行模型学习， 并能更加可靠地对新的轨迹进行外推