# A new local time-decoupled squared Wasserstein-2 method for training stochastic neural networks to reconstruct uncertain parameters in dynamical systems

arXiv: https://arxiv.org/abs/2503.05068 · HTML: https://mlsanity.com/paper/2503.05068/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 52 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Approximation Bounds for Random Neural Networks and Reservoir Systems](https://mlsanity.com/paper/2002.05933/) (2020)
- [Gaussian random field approximation via Stein's method with applications to wide random neural networks](https://mlsanity.com/paper/2306.16308/) (2023)
- [An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks](https://mlsanity.com/paper/2406.01653/) (2024)
- [Universal Approximation in Dropout Neural Networks](https://mlsanity.com/paper/2012.10351/) (2020)
- [Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN](https://mlsanity.com/paper/2110.13680/) (2021)

## Built on by (most cited first, 2 of 2)

- [A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks](https://mlsanity.com/paper/2507.05143/) (2025)
- [A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields](https://mlsanity.com/paper/2608.11613/) (2026)

## Abstract (arXiv)

In this work, we propose and analyze a new local time-decoupled squared Wasserstein-2 method for reconstructing the distribution of unknown parameters in dynamical systems. Specifically, we show that a stochastic neural network model, which can be effectively trained by minimizing our proposed local time-decoupled squared Wasserstein-2 loss function, is an effective model for approximating the distribution of uncertain model parameters in dynamical systems. Through several numerical examples, we showcase the effectiveness of our proposed method in reconstructing the distribution of parameters in different dynamical systems.