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

• URL: http://arxiv.org/abs/2404.15731v1
• Date: Wed, 24 Apr 2024 08:39:14 GMT
• Title: MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation
• Authors: Akshay Thakur, Souvik Chakraborty,
• Abstract summary: We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD) for 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 for output functions.
• Score: 0.9208007322096533
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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