An attempt to enhance flood inundation analysis using Physics-Informed Neural Net- works with hierarchical grid-based position encoding

Abstract

Physics-Informed Neural Networks (PINNs) that directly approximate the partial differential terms of coupled partial differential equations are a promising method for analyzing physical phenomena more quickly and with higher data reproducibility, potentially reducing computation times from as long as two days to just a few minutes. However, there are trade-offs between accuracy and speed due to (a) the de- pendence of error convergence on the strictness of physical laws, where ensuring the strictness of physical laws incurs greater computational loads-an important issue for the analysis of external water flooding in complex terrains; and (b) the inherent difficulty with clear terrain conditions since the entire spatiotemporal domain is represented as a continuous function, leaving many challenges in applying PINNs to real-world terrain problems.

In this study, by improving and introducing a hierarchical grid-based position embedding method called K-Plane into PINNs, we demonstrate that (a) it is possible to maintain high fidelity to physical laws while reducing the number of sampling points for calculating PINN losses, thus enabling faster computations; and (b) by pre-training K-Plane with terrain conditions, it is possible to represent water surfaces in accord- ance with natural terrain conditions, such as inside and outside levees. The feasibility of applying this method under real terrain conditions was confirmed. With terrain conditions and observational results, sim- ilar computations can be realized anywhere.