Physical Domain Reconstruction with Finite Volume Neural Networks

Abstract

The finite volume neural network (FINN) is an exception among recent physics-aware neural network models as it allows the specification of arbitrary boundary conditions (BCs). FINN can generalize and adapt to various prescribed BC values not provided during training, where other models fail. However, FINN depends explicitly on given BC values and cannot deal with unobserved parts within the physical domain. To overcome these limitations, we extend FINN in two ways. First, we integrate the capability to infer BC values on-the-fly from just a few data points. This allows us to apply FINN in situations, where the BC values, such as the inflow rate of fluid into a simulated medium, are unknown. Second, we extend FINN to plausibly reconstruct missing data within the physical domain via a gradient-driven spin-up phase. Our experiments validate that FINN reliably infers correct BCs, but also generates smooth and plausible full-domain reconstructions that are consistent with the observable data. Moreover, FINN can generate precise predictions orders of magnitude more accurate compared to competitive pure ML and physics-aware ML models – even when the physical domain is only partially visible, and the BCs are applied at a point that is spatially distant from the observable volumes.