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English(EN) Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization

Martingale Neural Operators 通过 Doob-Meyer 分解学习随机边际

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员开发了一种名为 Martingale Neural Operator (MNO) 的新型神经算子架构，旨在处理随机偏微分方程 (SPDE)。与现有塌缩为条件均值的确定性算子不同，MNO 利用 Doob-Meyer 定理直接将初始条件映射到终端定律的条件均值和协方差。这种方法通过恢复方差和尾部结构，实现了高效的不确定性量化，在 Wasserstein 距离和速度方面优于条件扩散基线。 AI

影响 引入了一种新颖的神经算子架构，可改进对随机系统的处理，可能推动科学建模中的不确定性量化。

排序理由 该集群包含一篇详细介绍新型模型架构的新学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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Martingale Neural Operators 通过 Doob-Meyer 分解学习随机边际

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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Kai Hidajat ·

    Martingale Neural Operators: 通过 Doob-Meyer 分解学习随机边际

    Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this structure typically requires Monte Carlo …

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