A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks

TL;DR

This paper introduces a generalized Wasserstein-2 distance method for training stochastic neural networks to efficiently reconstruct complex random field models with mixed variable types, demonstrating effectiveness in uncertainty quantification tasks.

Contribution

It presents a novel Wasserstein-2 based training approach for stochastic neural networks capable of modeling mixed random variables, with proven approximation capabilities and efficient training procedures.

Findings

Effective reconstruction of mixed random variables.

Successful application to uncertainty quantification tasks.

Proven approximation of random field models under Wasserstein-2.

Abstract

In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical components. We prove that a stochastic neural network can approximate random field models under a Wasserstein-2 distance metric under nonrestrictive conditions. Furthermore, this stochastic neural network can be efficiently trained by minimizing our proposed generalized local squared Wasserstein-2 loss function. We showcase the effectiveness of our proposed approach in various uncertainty quantification tasks, including classification, reconstructing the distribution of mixed random variables, and learning complex noisy dynamical systems from spatiotemporal data.