论文标题
界限傅立叶神经操作员的rademacher复杂性
Bounding the Rademacher Complexity of Fourier neural operators
论文作者
论文摘要
傅立叶神经操作员（FNO）是物理启发的机器学习方法之一。特别是它是一个神经操作员。最近，已经开发了几种类型的神经操作员，例如，深度操作员网络，图形神经操作员（GNO）和基于多波管的操作员（MWTO）。与其他模型相比，FNO在计算上是有效的，并且可以在功能空间之间学习非线性操作员，而不是一定有限的基础。在这项研究中，我们根据特定组规范研究了FNO的Rademacher复杂性的边界。使用基于这些规范的容量，我们限制了模型的概括误差。此外，我们研究了经验概括误差与提议的FNO能力之间的相关性。从我们的结果的角度来看，我们推断出组规范的类型决定了以容量存储的FNO模型的权重和体系结构的信息。然后，我们通过实验证实了这些推论。基于这个事实，我们深入了解了FNO模型中使用的模式数量对概括误差的影响。我们获得了遵循我们见解的实验结果。
A Fourier neural operator (FNO) is one of the physics-inspired machine learning methods. In particular, it is a neural operator. In recent times, several types of neural operators have been developed, e.g., deep operator networks, Graph neural operator (GNO), and Multiwavelet-based operator (MWTO). Compared with other models, the FNO is computationally efficient and can learn nonlinear operators between function spaces independent of a certain finite basis. In this study, we investigated the bounding of the Rademacher complexity of the FNO based on specific group norms. Using capacity based on these norms, we bound the generalization error of the model. In addition, we investigated the correlation between the empirical generalization error and the proposed capacity of FNO. From the perspective of our result, we inferred that the type of group norms determines the information about the weights and architecture of the FNO model stored in the capacity. And then, we confirmed these inferences through experiments. Based on this fact, we gained insight into the impact of the number of modes used in the FNO model on the generalization error. And we got experimental results that followed our insights.
