Hybrid Boundary Physics-Informed Neural Networks for Solving Navier-Stokes Equations with Complex Boundary

TL;DR

This paper introduces a Hybrid Boundary PINN method that combines pretrained networks and boundary constraints to effectively solve Navier-Stokes equations with complex boundary conditions, achieving state-of-the-art accuracy.

Contribution

The novel HB-PINN approach integrates boundary-aware mechanisms with pretrained networks, improving solution accuracy for complex boundary Navier-Stokes problems.

Findings

Achieves state-of-the-art results on benchmark Navier-Stokes problems.

Significantly improves accuracy over existing PINN methods.

Effectively handles complex boundary conditions in fluid flow simulations.

Abstract

Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper, we introduce a novel Hybrid Boundary PINN (HB-PINN) method that combines a pretrained network for efficient initialization with a boundary-constrained mechanism. The HB-PINN method features a primary network focused on inner domain points and a distance metric network that enhances predictions at the boundaries, ensuring accurate solutions for both boundary and interior regions. Comprehensive experiments have been conducted on the NSE under complex boundary conditions, including the 2D cylinder wake flow and the 2D blocked cavity flow with a segmented inlet. The proposed method achieves state-of-the-art (SOTA) performance on these benchmark scenarios, demonstrating significantly improved accuracy over existing PINN-based approaches.