  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.
