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English(EN) Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

新的神经网络方法解决复杂的偏微分方程 · 跟踪 3 个来源

作者 PulseAugur 编辑部 · [3 个来源] ·

研究人员开发了用于求解复杂域中偏微分方程 (PDE) 的新神经网络框架。一种方法，域分解随机神经网络，使用近场和远场区域的专用子网络来更准确地处理无界域。另一种方法，PCA--RaNN，将基于 PCA 的降维与随机特征相结合，以实现神经网络算子更快的训练，在保持精度的同时实现显著加速，并实现不确定性量化。 AI

影响 这些进展可以加速科学工作流程，并提高依赖于求解复杂微分方程的领域的模拟精度。

排序理由 该集群包含两篇关于求解偏微分方程的新型神经网络架构的研究论文。

在 arXiv cs.LG 阅读 →

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新的神经网络方法解决复杂的偏微分方程 · 跟踪 3 个来源

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该集群包含两篇关于求解偏微分方程的新型神经网络架构的研究论文。
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报道来源 [3]

  1. arXiv cs.LG TIER_1 English(EN) · Haixin Wang, Haoning Dang, Fei Wang, Shimin Guo ·

    无界域偏微分方程的域分解随机神经网络

    arXiv:2606.31342v1 Announce Type: cross Abstract: Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods often require problem-dependent artificial boundary c…

  2. arXiv cs.LG TIER_1 English(EN) · Shimin Guo ·

    无界域偏微分方程的域分解随机神经网络

    Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods often require problem-dependent artificial boundary conditions, while global spectral bases may be inef…

  3. arXiv cs.LG TIER_1 English(EN) · Zirui Deng, Jingbo Sun, Deyu Meng, Fei Wang ·

    参数化偏微分方程的随机神经算子，具有快速训练和共形不确定性量化

    arXiv:2606.29440v1 Announce Type: new Abstract: Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training. We introduce PCA--RaNN, a randomized …

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