English

MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation

Machine Learning 2025-05-13 v2

Abstract

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.

Keywords

Cite

@article{arxiv.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}
}
R2 v1 2026-06-28T16:04:51.257Z