Abstract
When modeling physical processes in spatially confined domains, the boundaries require distinct consideration through specifying appropriate boundary conditions (BCs). The finite volume neural network (FINN) is an exception among recent physics-aware neural network models: it allows the specification of arbitrary BCs. FINN is even able to generalize to modified BCs not seen during training, but requires them to be known during prediction. However, so far even FINN was not able to handle unknown BC values. Here, we extend FINN in order to infer BC values on-the-fly. This allows us to apply FINN in situations, where the BC values, such as the inflow rate of fluid into a simulated medium, is unknown. Experiments validate FINN’s ability to not only infer the correct values, but also to model the approximated Burgers’ and Allen-Cahn equations with higher accuracy compared to competitive pure ML and physics-aware ML models. Moreover, FINN generalizes well beyond the BC value range encountered during training, even when trained on only one fixed set of BC values. Our findings emphasize FINN’s ability to reveal unknown relationships from data, thus offering itself as a process-explaining system.
This work was partially funded by German Research Foundation (DFG) under Germany’s Excellence Strategy - EXC 2075 - 390740016 as well as EXC 2064 - 390727645. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). Moreover, we thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Matthias Karlbauer.
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Horuz, C.C. et al. (2022). Infering Boundary Conditions in Finite Volume Neural Networks. In: Pimenidis, E., Angelov, P., Jayne, C., Papaleonidas, A., Aydin, M. (eds) Artificial Neural Networks and Machine Learning – ICANN 2022. ICANN 2022. Lecture Notes in Computer Science, vol 13529. Springer, Cham. https://doi.org/10.1007/978-3-031-15919-0_45
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