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Effective inclusion of physics-based knowledge into deep neural networkmodels of dynamical systems can greatly improve data efficiency andgeneralization. Such a-priori knowledge might arise from physical principles(e.g., conservation laws) or from the system's design (e.g., the Jacobianmatrix of a robot), even if large portions of the system dynamics remainunknown. We develop a framework to learn dynamics models from trajectory datawhile incorporating a-priori system knowledge as inductive bias. Morespecifically, the proposed framework uses physics-based side information toinform the structure of the neural network itself, and to place constraints onthe values of the outputs and the internal states of the model. It representsthe system's vector field as a composition of known and unknown functions, thelatter of which are parametrized by neural networks. The physics-informedconstraints are enforced via the augmented Lagrangian method during the model'straining. We experimentally demonstrate the benefits of the proposed approachon a variety of dynamical systems -- including a benchmark suite of roboticsenvironments featuring large state spaces, non-linear dynamics, externalforces, contact forces, and control inputs. By exploiting a-priori systemknowledge during training, the proposed approach learns to predict the systemdynamics two orders of magnitude more accurately than a baseline approach thatdoes not include prior knowledge, given the same training dataset.

Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling