Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation
arXiv:2605.24041v1 Announce Type: new Abstract: Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), which augments pre-trained operators with a learned refinement module iteratively applied via fixed-point iteration. IRNO decomposes the prediction into a coarse initialization followed by successive residual corrections, paralleling classical numerical so
The continuous drive for more accurate and efficient AI models in scientific computing, particularly to overcome limitations like spectral bias, makes this iterative refinement approach a timely development.
This development offers a principled method to improve the accuracy of neural operators, crucial for reliable high-fidelity scientific simulations and potentially broadening AI's application in complex physical systems.
The inference procedure for neural operators shifts from a single-pass method to an iterative, fixed-point approach, leading to better resolution of high-frequency details and mitigating spectral bias.
- · Scientific computing researchers
- · Engineering simulation software providers
- · AI model developers
- · Industries relying on complex simulations (e.g., aerospace, pharmaceuticals)
- · Developers of less accurate, single-pass neural operators
- · Methods that cannot resolve fine-grained details efficiently
Scientific simulations become significantly more accurate and reliable, reducing the need for costly physical prototypes or experiments.
This improved accuracy accelerates research and development cycles across various scientific and engineering disciplines.
The enhanced capability for data-driven surrogates could lead to new discoveries or designs previously unattainable due to computational limitations or modeling inaccuracies.
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Read at arXiv cs.LG