Technology Category
Search and Optimization: Mixed Discrete/Continuous SearchMachine Learning: Learning on the Edge & Model CompressionConstraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks
🤖 AI Summary
Physical-informed neural networks (PINNs) suffer from inaccurate enforcement of Dirichlet boundary conditions, leading to large boundary errors and unstable convergence. To address this, we propose a hybrid FEM-PINN framework that embeds the finite element method (FEM) within a boundary-adjacent region to construct a hard boundary constraint mechanism—enabling the first-ever strong imposition of Dirichlet conditions in PINNs. This approach departs from conventional soft-constraint paradigms while preserving strict physical consistency with the underlying PDEs. Evaluated across six PDE benchmarks with progressively increasing geometric complexity, our method reduces boundary errors by one to two orders of magnitude, accelerates convergence, and enhances training robustness. The framework demonstrates strong generalizability to industrial-scale PDE problems involving complex geometries.
Technology Category
Application Category
📝 Abstract
Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.
Problem
Research questions and friction points this paper is trying to address.
PINNs
Dirichlet boundary conditions
Computational accuracy and stability
Innovation
Methods, ideas, or system contributions that make the work stand out.
PINN-FEM
Boundary Condition Handling
Complex Environment PDE Solving
🔎 Similar Papers
No similar papers found.
