  Effective inclusion of physics-based knowledge into deep neural network
models of dynamical systems can greatly improve data efficiency and
generalization. Such a-priori knowledge might arise from physical principles
(e.g., conservation laws) or from the system's design (e.g., the Jacobian
matrix of a robot), even if large portions of the system dynamics remain
unknown. We develop a framework to learn dynamics models from trajectory data
while incorporating a-priori system knowledge as inductive bias. More
specifically, the proposed framework uses physics-based side information to
inform the structure of the neural network itself, and to place constraints on
the values of the outputs and the internal states of the model. It represents
the system's vector field as a composition of known and unknown functions, the
latter of which are parametrized by neural networks. The physics-informed
constraints are enforced via the augmented Lagrangian method during the model's
training. We experimentally demonstrate the benefits of the proposed approach
on a variety of dynamical systems -- including a benchmark suite of robotics
environments featuring large state spaces, non-linear dynamics, external
forces, contact forces, and control inputs. By exploiting a-priori system
knowledge during training, the proposed approach learns to predict the system
dynamics two orders of magnitude more accurately than a baseline approach that
does not include prior knowledge, given the same training dataset.
