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English(EN) Self-composing neural operators for high-frequency and multiscale PDE surrogates

新的神经算子框架处理复杂的偏微分方程 · 2篇论文

作者 PulseAugur 编辑部 · [3 个来源] ·

两篇新的研究论文介绍了一种用于求解偏微分方程（PDE）的新型神经算子框架。第一篇，FB-C2CNet，利用固定基来编码和解码函数系数，降低了可训练维度和训练成本，同时适应散乱数据。第二篇，SC-NO，采用自组合架构，迭代应用骨干模块，模仿经典迭代求解器，逐步解析复杂的解特征，并减轻频谱偏差，特别适用于高频和多尺度问题。 AI

影响 引入了新的神经算子架构，可以提高解决复杂数学问题的效率和准确性。

排序理由 两篇学术论文发表在arXiv上，介绍了求解偏微分方程的新方法。

在 arXiv cs.LG 阅读 →

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新的神经算子框架处理复杂的偏微分方程 · 2篇论文

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两篇学术论文发表在arXiv上，介绍了求解偏微分方程的新方法。
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报道来源 [3]

  1. arXiv cs.AI TIER_1 English(EN) · Shengxin Kong, Liwen Xu, Jingwen Fu ·

    使用领域特定语言改进神经偏微分方程求解器的自动设计

    arXiv:2608.04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem. In the space of unrestricted Python programs, valid solvers form an extremely sparse subset: most candidate programs are syntactically incorrect, …

  2. arXiv cs.LG TIER_1 English(EN) · Chuqi Chen, Yang Xiang, Weihong Zhang ·

    用于偏微分方程的处方基系数到系数神经网络算子

    arXiv:2510.10350v3 Announce Type: replace-cross Abstract: Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and output functions are represented. Point-value…

  3. arXiv cs.LG TIER_1 English(EN) · Juncai He, Xinliang Liu, Jinchao Xu ·

    用于高频和多尺度偏微分方程代理的自组成神经网络算子

    arXiv:2508.20650v2 Announce Type: replace Abstract: Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framework. Inspired by classical fixed-point iterative…

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