测试时通过组合已有模型实现物理方程零样本泛化。
Test-time Generalization for Physics through Neural Operator Splitting
- 测试时动态组合预训练神经算子，逼近未知物理规律。
- 在参数外推和新物理组合任务上达到当前最佳零样本性能。
- 无需微调即可恢复隐含的偏微分方程参数，适合快速部署。
神经算子在学习偏微分方程（PDE）解映射方面表现优异，但在测试输入超出训练分布时（如新初始条件、未见的PDE系数或新物理现象）常出现泛化失败。现有方法依赖大规模多物理预训练+微调，仍需新动力学样例，难以实现真正的零样本泛化。本文提出一种测试时增强泛化的方法，不修改预训练权重。基于DISCO框架（跨多种动力学训练的神经算子字典），引入神经算子拆分策略：测试时搜索训练算子的组合，以逼近未知动力学。在具有挑战性的分布外任务（包括参数外推和新物理现象组合）中，该方法实现了最先进的零样本泛化效果，并能恢复底层的PDE参数。结果表明，测试时计算是构建灵活、可组合、强泛化的神经算子的关键路径。
原文摘要 · Abstract (English)
Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics. Prior works address this limitation with large-scale multiple physics pretraining followed by fine-tuning, but this still require examples from the new dynamics, falling short of true zero-shot generalization. In this work, we propose a method to enhance generalization at test time, i.e., without modifying pretrained weights. Building on DISCO, which provides a dictionary of neural operators trained across different dynamics, we introduce a neural operator splitting strategy that, at test time, searches over compositions of training operators to approximate unseen dynamics.On challenging out-of-distribution tasks including parameter extrapolation and novel combinations of physics phenomena, our approach achieves state-of-the-art zero-shot generalization results, while being able to recover the underlying PDE parameters. These results underscore test-time computation as a key avenue for building flexible, compositional, and generalizable neural operators.
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