🤖 AI Summary
This study addresses the structural degradation of pretrained neural operators during simulation-to-real (Sim2Real) transfer and proposes the R²NO framework. The method freezes the fine-tuned source predictor and introduces a shared repair module, innovatively formulating adaptation depth as the selective activation of Fourier-domain units learned independently from real data. It further integrates orthogonal Fourier projection, spectral ensembling, and ridge regression to fuse multiple candidate refinements. Experiments on RealPDEBench across six backbone architectures demonstrate that R²NO consistently outperforms full fine-tuning and iterative refinement baselines, achieving robust Sim2Real transfer for neural operators.
📝 Abstract
Neural operators increasingly benefit from pretraining on numerical simulations, yet adapting them for real-world prediction remains challenging. We introduce the Retain-and-Repair Neural Operator (R$^2$NO), a framework for adapting simulation-pretrained operators to real-world data while retaining useful pretrained structure. The pretrained operator is first finetuned on real data and then frozen to provide a source prediction, and a shared repair module learns a sequence of refinements from the same observations. Using orthogonal Fourier projections, a spectral ensemble fits a small ridge regression within each cell of the Fourier domain and combines the refinements by weights fitted on a held-out split of the real data. The cells are defined jointly by radial ranges, angular sectors, and measured channels, allowing refinement depth to vary with frequency magnitude, with orientation, and across channels. Including the source prediction as a candidate makes retention available in every cell, and independently trained repair modules enter the same combination as additional candidates. On all RealPDEBench systems and six backbones, R$^2$NO consistently outperforms full finetuning and iterative refinement. The framework treats adaptation depth as a cell-specific choice learned from real data.