MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation
<|reference_start|>MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation: 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.<|reference_end|>
@article{thakur2024md-nomad:,
    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={2024},
    archivePrefix={arXiv},
    eprint={2404.15731},
    primaryClass={cs.LG}
}