发表机构
TelePIX（TelePIX）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出保留-修复神经算子（R$^2$NO），通过冻结微调后的源预测并学习谱域单元级修复，在真实数据上自适应地改进仿真预训练模型，显著超越完全微调。
AI 中文摘要
神经算子越来越多地受益于在数值模拟上的预训练，但将其适应于真实世界预测仍具挑战性。我们引入了保留-修复神经算子（R$^2$NO），一个将仿真预训练算子适应到真实世界数据同时保留有用预训练结构的框架。预训练算子首先在真实数据上进行微调，然后被冻结以提供源预测，一个共享的修复模块从相同的观测中学习一系列改进。利用正交傅里叶投影，一个谱集成在傅里叶域的每个单元内拟合一个小型岭回归，并通过在真实数据的保留分割上拟合的权重组合这些改进。这些单元由径向范围、角度扇区和测量通道共同定义，允许改进深度随频率幅度、方向和通道变化。将源预测作为候选包含在内使得在每个单元中都可进行保留，独立训练的修复模块作为额外候选进入相同的组合。在所有RealPDEBench系统和六个骨干网络上，R$^2$NO始终优于完全微调和迭代改进。该框架将适应深度视为从真实数据中学习的单元特定选择。
英文摘要
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.
