arXiv:2508.02537v3 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) offer a powerful framework for solving PDEs by embedding physical laws into the learning process. However, when applied to domains with irregular boundaries, PINNs often suffer from instability and slow convergence, which stems from (1) inconsistent normalization due to geometric anisotropy, (2) inaccurate boundary enforcement, and (3) imbalanced loss term competition. A common workaround is to map the domain to a regular space. Yet, conventional mapping methods rely on case-specific meshes, define Jac
The continuous evolution of AI in solving complex scientific and engineering problems pushes the boundaries of computational methods, addressing existing limitations in areas like irregular domain modeling.
Improving the stability and convergence of Physics-Informed Neural Networks (PINNs) in complex geometries accelerates their application in critical fields, potentially reducing R&D cycles and enhancing simulation accuracy.
The introduction of JacobiNet provides a more robust and generalizable method for applying PINNs to irregular domains, overcoming prior issues of instability, slow convergence, and reliance on case-specific mesh generation.
- · Computational fluid dynamics researchers
- · Material science engineers
- · AI/ML researchers in scientific computing
- · Aerospace engineering
- · Traditional mesh generation software reliant on manual tuning
- · Computational engineers without AI/ML expertise
More accurate and faster simulations become possible for complex physical systems with irregular boundaries.
Accelerated discovery and design processes in fields like manufacturing, drug discovery, and environmental modeling due to improved simulation capabilities.
Enhanced AI foundation models for scientific discovery, leading to unforeseen breakthroughs in interdisciplinary research and industrial applications.
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Read at arXiv cs.LG