用专家混合方法同时学习边界条件和自动选模型，提升物理模拟泛化能力。
Mixture of neural operator experts for learning boundary conditions and model selection
- 引入竞争性专家机制，结合体积惩罚思想实现灵活边界处理
- 在圆盘和四分之一圆盘上成功恢复非线性算子，验证方法有效性
- 适用于需要模型选择与长期预测的复杂流体模拟场景
虽然基于傅里叶的神经算子最适合周期域上的函数映射，但已有方法在处理非平凡边界条件时存在局限。本文受数值方法中的体积惩罚和机器学习中的专家混合（MoE）启发，提出一种新方法：通过引入竞争性专家，不仅可有效施加边界条件，还支持模型选择。我们结合空间条件化的MoE与基于傅里叶的模态算子回归物理（MOR-Physics）神经算子，在圆盘和四分之一圆盘上恢复了非线性算子。进一步，从通道流的直接数值模拟（DNS）中提取大涡模拟（LES）模型，并利用该方法实现域分解。最后，采用贝叶斯变分推断训练该LES模型，获得了远超原始DNS时间跨度的后验预测样本。
原文摘要 · Abstract (English)
While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced methods have restrictions that limit their applicability. In this work, we introduce an alternative approach to imposing boundary conditions inspired by volume penalization from numerical methods and Mixture of Experts (MoE) from machine learning. By introducing competing experts, the approach additionally allows for model selection. To demonstrate the method, we combine a spatially conditioned MoE with the Fourier based, Modal Operator Regression for Physics (MOR-Physics) neural operator and recover a nonlinear operator on a disk and quarter disk. Next, we extract a large eddy simulation (LES) model from direct numerical simulation of channel flow and show the domain decomposition provided by our approach. Finally, we train our LES model with Bayesian variational inference and obtain posterior predictive samples of flow far past the DNS simulation time horizon.
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