Discrete-time Physics-Informed Neural Networks for Two-Phase Flow Interface Capturing

Zhuo Zhang

Abstract: Physics-informed neural networks (PINNs) have recently emerged as a powerful paradigm for modeling complex physical phenomena underlying visual dynamics, such as fluid motion and deformation. However, training PINNs remains challenging due to gradient inconsistencies across PDE, boundary, and initial constraints, which hinder scalability to large and complex visual domains. To address this issue, we propose the Dual-Gradient Co-Optimization Physics-Informed Neural Network (DGCO-PINN), a novel framework that jointly adjusts internal and external gradient dynamics. Specifically, DGCO-PINN refines internal parameter gradients through Hierarchical Gradient Enhancement (HGE) and harmonizes external loss gradients via a two-stage gradient resonance weighting strategy. This dual optimization quantitatively measures the difficulty of each physical constraint, ensuring balanced convergence and alleviating internal gradient pathologies. Extensive experiments on benchmark PDE problems demonstrate that DGCO-PINN achieves faster convergence and higher predictive accuracy than existing gradient-statistics-based baselines.