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

Abstract

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