A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909677595394048 |
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| author | Xia, Mingtao Shen, Qijing |
| author_facet | Xia, Mingtao Shen, Qijing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks Xia, Mingtao Shen, Qijing Machine Learning 60A05, 68Q87, 65C99 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. |
| title | A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks |
| topic | Machine Learning 60A05, 68Q87, 65C99 |
| url | https://arxiv.org/abs/2507.05143 |