Retain and repair neural operators improve real world simulation predictions
Beyond Simulation: Retain-and-Repair Neural Operators for Real-World Adaptation
Machine Learning
Summary
Neural operators are tools trained on computer simulations to predict complex systems, but they often struggle to work well with real-world data. The authors introduce a method called Retain-and-Repair Neural Operator (R2NO) that first fine-tunes these tools on real data and then uses a repair module to make detailed improvements. This approach keeps useful parts of the original model while adapting it better to real-world situations. Testing showed that R2NO outperforms existing methods on various benchmark problems.
What this means in practice
- •For engineering simulation teams: Improve predictive models for real-world engineering systems by adapting simulation-trained neural operators without losing useful pretrained features.
- •For environmental modeling teams: Enhance accuracy of climate and fluid dynamics predictions by refining pretrained models with small real-world datasets using a repair approach.
Authors
Woojin Cho, Junghwan Park
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.