A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks
This provides an efficient method for uncertainty quantification in complex systems with mixed data types, though it appears incremental as an extension of Wasserstein distances to specific neural network training.
The authors tackled the problem of reconstructing random field models with mixed continuous and categorical variables by proposing a generalized Wasserstein-2 distance approach for training stochastic neural networks, proving approximation capabilities under nonrestrictive conditions and demonstrating effectiveness in uncertainty quantification tasks.
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.