Long‐lead forecasting for spatio‐temporal systems can entail complex nonlinear dynamics that are difficult to specify a priori. Current statistical methodologies for modeling these processes are often highly parameterized and, thus, challenging to implement from a computational perspective. One potential parsimonious solution to this problem is a method from the dynamical systems and engineering literature referred to as an echo state network (ESN). ESN models use
Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling
Effective inclusion of physics-based knowledge into deep neural network models of dynamical sys- tems 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 featur- ing 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.
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- Award ID(s):
- 1646522
- NSF-PAR ID:
- 10383170
- Editor(s):
- Firoozi, R.; Mehr, N.; Yel, E.; Antonova, R.; Bohg, J.; Schwager, M.; Kochenderfer, M.
- Date Published:
- Journal Name:
- 4th Annual Conference on Learning for Dynamics and Control
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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