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[2602.19265] Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines
Summary
This paper explores spectral bias in physics-informed neural networks and operator learning, analyzing its causes and offering mitigation strategies to improve high-frequency mode recovery in solutions to partial differential equations.
Why It Matters
Understanding spectral bias is crucial for enhancing the performance of neural networks in solving complex physical problems. This research provides insights into optimizing architectures and loss functions, which can lead to more accurate predictions in various scientific applications, including fluid dynamics and earthquake modeling.
Key Takeaways
- Spectral bias affects the learning speed of low vs. high-frequency components in neural networks.
- Optimization strategies, particularly second-order methods, can significantly improve high-frequency mode recovery.
- Mitigating spectral bias can be achieved through tailored loss functions without increasing inference costs.
Computer Science > Machine Learning arXiv:2602.19265 (cs) [Submitted on 22 Feb 2026] Title:Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines Authors:Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari, Maxim Beekenkamp, George Em Karniadakis View a PDF of the paper titled Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines, by Siavash Khodakarami and 4 other authors View PDF HTML (experimental) Abstract:Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit spectral bias, whereby low-frequency components of the solution are learned significantly faster than high-frequency modes. While spectral bias is often treated as an intrinsic representational limitation of neural architectures, its interaction with optimization dynamics and physics-based loss formulations remains poorly understood. In this work, we provide a systematic investigation of spectral bias in physics-informed and operator learning frameworks, with emphasis on the coupled roles of network architecture, activation functions, loss design, and optimization strategy. We quantify spectral bias through frequency-resolved error metrics, Barron-norm diagnostics, and higher-order statistical moments, enabling a unified analysis across elliptic, hyp...
