We propose a neural operator framework, termed mixture density nonlinear
manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages
an amalgamation of the pointwise operator learning neural architecture
nonlinear manifold decoder (NOMAD) with mixture density-based methods to
estimate conditional probability distributions for stochastic output functions.
MD-NOMAD harnesses the ability of probabilistic mixture models to estimate
complex probability and the high-dimensional scalability of pointwise neural
operator NOMAD. We conduct empirical assessments on a wide array of stochastic
ordinary and partial differential equations and present the corresponding
results, which highlight the performance of the proposed framework.

我们提出了一种神经算子框架，称为混合密度非线性流形解码器（MD-NOMAD），用于随机模拟器。我们的方法利用了点对点算子学习神经结构非线性流形解码器（NOMAD）与基于混合密度的方法的融合，用于估计随机输出函数的条件概率分布。MD-NOMAD 利用概率混合模型估计复杂概率和点对点神经算子 NOMAD 的高维扩展性。我们对广泛的随机常微分方程和偏微分方程进行了实证评估，并展示了相应的结果，突出了该框架的性能。