In this paper, we construct a mixture of neural operators (MoNOs) between function spaces whose complexity is distributed over a network of expert neural operators (NOs), with each NO satisfying parameter scaling restrictions. Our main result is a \textit{distributed} universal approximation theorem guaranteeing that any Lipschitz non-linear operator between $L^2([0,1]^d)$ spaces can be approximated uniformly over the Sobolev unit ball therein, to any given $\varepsilon>0$ accuracy, by an MoNO while satisfying the constraint that: each expert NO has a depth, width, and rank of $\mathcal{O}(\varepsilon^{-1})$. Naturally, our result implies that the required number of experts must be large, however, each NO is guaranteed to be small enough to be loadable into the active memory of most computers for reasonable accuracies $\varepsilon$. During our analysis, we also obtain new quantitative expression rates for classical NOs approximating uniformly continuous non-linear operators uniformly on compact subsets of $L^2([0,1]^d)$.

我们建立了一个混合神经算子（MoNOs），它在功能空间之间构建复杂性由专家神经算子（NOs）网络分布。我们的主要结果是一个“分布式”通用逼近定理，保证可以通过MoNO以任意给定的ε精度均匀逼近在其中的Sobolev单位球上的任何Lipschitz非线性算子，并满足每个专家NO的深度、宽度和秩为Ο(ε^(-1))的约束。我们的结果还证明了经典NO在L^2([0,1]^d)的紧致子集上均匀逼近连续非线性算子的新的定量表达速率。

混合专家软化算子学习中的维度灾难