AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition

2025-10-09

AI Summary

Traditional physics-informed neural networks (PINNs) with fixed domain decomposition lack adaptivity in solving multiscale partial differential equations (PDEs), failing to align with the intrinsic multiscale structure of solutions. Method: We propose Adaptive Basis PINN (AB-PINN), which introduces a residual-driven dynamic domain decomposition mechanism inspired by numerical mesh refinement: subdomains are generated and adjusted in real time during training based on local PDE residuals, enabling co-evolution of subdomain distribution and solution features. A parameter-sharing and collaborative optimization framework across subdomains enhances representational capacity and mitigates local minima. Contribution/Results: AB-PINN achieves superior accuracy and convergence stability on multiple benchmark problems involving strongly nonlinear, multiscale PDEs—requiring less hyperparameter tuning than baseline methods—demonstrating enhanced robustness and generalization capability.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Multiagent Systems: Adversarial Agents
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing inspiration from classical mesh refinement techniques, we also modify the domain decomposition on-the-fly throughout training by introducing new subdomains in regions of high residual loss, thereby providing additional expressive power where the solution of the differential equation is challenging to represent. Our flexible approach to domain decomposition is well-suited for multiscale problems, as different subdomains can learn to capture different scales of the underlying solution. Moreover, the ability to introduce new subdomains during training helps prevent convergence to unwanted local minima and can reduce the need for extensive hyperparameter tuning compared to static domain decomposition approaches. Throughout, we present comprehensive numerical results which demonstrate the effectiveness of AB-PINNs at solving a variety of complex multiscale partial differential equations.

Problem

• Dynamic domain decomposition adapts to solution features in PINNs
• Introducing new subdomains in high residual regions during training
• Solving multiscale PDEs while preventing local minima convergence

Innovation

• Dynamic subdomain adaptation to solution features
• On-the-fly domain decomposition in high-loss regions
• Flexible domain decomposition for multiscale problems