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

arXiv: https://arxiv.org/abs/2507.05143 · HTML: https://mlsanity.com/paper/2507.05143/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/2108.13054/) (2021)
- [An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks](https://mlsanity.com/paper/2406.01653/) (2024)
- [Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations](https://mlsanity.com/paper/2401.11354/) (2024)
- [A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty](https://mlsanity.com/paper/2406.06825/) (2024)
- [A new local time-decoupled squared Wasserstein-2 method for training stochastic neural networks to reconstruct uncertain parameters in dynamical systems](https://mlsanity.com/paper/2503.05068/) (2025)

## Abstract (arXiv)

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.