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.
View on arXiv@article{thakur2025_2404.15731,
title={ MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation },
author={ Akshay Thakur and Souvik Chakraborty },
journal={arXiv preprint arXiv:2404.15731},
year={ 2025 }
}