Iterative Refinement Neural Operators Improve Spectral Bias in Scientific Modeling
A new paper on arXiv introduces the Iterative Refinement Neural Operator (IRNO), a method that enhances pre-trained neural operators by adding a learned refinement module applied through fixed-point iteration. This approach addresses spectral bias, the difficulty neural operators have in resolving high-frequency details. IRNO decomposes predictions into a coarse initialization followed by successive residual corrections, similar to classical numerical solvers. Under local assumptions, the induced operator is proven to contract, ensuring convergence to a unique fixed point. A progressive spectral loss is proposed to adaptively increase penalties on high-frequency components during training. Tests across physical systems show consistent error reduction, with improvements up to 56.05%.
Key facts
- IRNO augments pre-trained operators with a learned refinement module via fixed-point iteration.
- The method decomposes prediction into coarse initialization and successive residual corrections.
- Contraction of the induced operator ensures convergence to a unique fixed point under local assumptions.
- A progressive spectral loss adaptively increases penalty on high-frequency components during training.
- IRNO achieves up to 56.05% improvement in error reduction across physical systems.
- The paper is published on arXiv with ID 2605.24041.
- The approach parallels classical numerical solvers.
- Spectral bias refers to the limitation of neural operators in resolving high-frequency details.
Entities
Institutions
- arXiv