A fundamental study on learning strategies for PINNs and the applicability of a PINN-GCN architecture to unsteady groundwater flow analysis

Abstract

In this study, we investigate the effectiveness of training strategies and network architectures for physics-informed neural networks (PINNs) applied to transient groundwater flow analysis. We focus on three PINN training methods: Causal Gate, Gradient based loss balancing, and R3 sampling as PINNs training methods. We also evaluate their individual and combined effects. As for network architectures, we compare multilayer perceptron–based PINNs (PINN-MLP) with graph convolutional network–based PINNs (PINN-GCN). Our results show that combining gradient based loss balancing with causal gate significantly enhances both training stability and estimation accuracy. Moreover, under limited observational conditions (five spatial points within a 1 km² area and 49 temporal points), the optimized PINN-MLP outperforms PINN-GCN, achieving an R2 =0.943 against the analytical solution. This study demonstrates the effectiveness of optimizing training strategies and MLP - based architectures for modeling of transient groundwater flow.