Surrogate-data-enriched Physics-Aware Neural Networks
This addresses data scarcity in complex physics simulations for researchers and engineers, but it is incremental as it builds on existing physics-aware methods.
The paper tackles the problem of scarce expensive data for physics-aware neural networks by enriching them with cheaper but inexact data from surrogate models like Reduced-Order Models, and shows that training accuracy increases by two orders of magnitude for the one-dimensional wave equation.
Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to additionally respect data from numerical simulations or experiments in the training process. However, this data is frequently expensive to obtain and thus only scarcely available for complex models. In this work, we investigate how physics-aware models can be enriched with computationally cheaper, but inexact, data from other surrogate models like Reduced-Order Models (ROMs). In order to avoid trusting too-low-fidelity surrogate solutions, we develop an approach that is sensitive to the error in inexact data. As a proof of concept, we consider the one-dimensional wave equation and show that the training accuracy is increased by two orders of magnitude when inexact data from ROMs is incorporated.