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[2602.16193] Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings
Summary
This article presents a novel approach to enhance Physics-Informed Neural Networks (PINNs) by utilizing geometric compactification mappings to improve convergence and accuracy in solving multi-scale PDEs.
Why It Matters
The research addresses significant challenges in training PINNs, particularly the issues of gradient stiffness and ill-conditioning caused by fixed coordinate systems. By introducing a new mapping paradigm, this work has the potential to improve the performance of neural networks in complex physical simulations, which is crucial for advancements in scientific computing and engineering applications.
Key Takeaways
- Introduces Geometric Compactification (GC)-PINN framework to enhance training stability.
- Addresses gradient stiffness and convergence issues in existing PINN methods.
- Demonstrates improved accuracy and uniform residual distributions in PDE solutions.
Computer Science > Machine Learning arXiv:2602.16193 (cs) [Submitted on 18 Feb 2026] Title:Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings Authors:Zhenzhen Huang, Haoyu Bian, Jiaquan Zhang, Yibei Liu, Kuien Liu, Caiyan Qin, Guoqing Wang, Yang Yang, Chaoning Zhang View a PDF of the paper titled Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings, by Zhenzhen Huang and 8 other authors View PDF HTML (experimental) Abstract:Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN) methods typically train with fixed coordinate system inputs, where geometric misalignment with these structures induces gradient stiffness and ill-conditioning that hinder convergence. To address this issue, we introduce a mapping paradigm that reshapes the input coordinates through differentiable geometric compactification mappings and couples the geometric structure of PDEs with the spectral properties of residual operators. Based on this paradigm, we propose Geometric Compactification (GC)-PINN, a framework that introduces three mapping strategies for periodic boundaries, far-field scale expansion, and localized singular structures in the input domain without modifying the underlying PINN architecture. Extensive empirica...
