Differential Equations as a Model Prior for Deep Learning and its Applications in Robotics

For many decades, much of the scientific knowledge of physics and engineering has been expressed via differential equations. These differential equations describe the underlying phenomena and the relations between different interpretable quantities. Therefore, differential equations are a promising approach to incorporate prior knowledge in machine learning models to obtain robust and interpretable models. Especially, deep networks and differential equations fit naturally as deep networks are differentiable and enable the computation of the partial derivatives in closed form at machine precision (Raissi & Karniadakis, 2018). Therefore, combining deep networks and differential equations is a promising approach to constrain deep networks to learn meaningful representations.