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English(EN) Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

新研究详细介绍了基于核的算子学习，包含误差分析和物理信息扩展

作者 PulseAugur 编辑部 · [4 个来源] ·

研究人员发表了关于基于核的算子学习的新工作，详细介绍了误差分析和预算分配策略。该研究引入了一个涉及离线回归和在线重构算子的两阶段框架，并建立了平衡训练数据、输入观测和输出分辨率的条件。此外，还提出了一种物理信息扩展，该扩展在不重新训练的情况下融入了偏微分方程的知识，并通过数值实验证明了其有效性。 AI

影响 推进了算子学习的理论理解，可能提高AI模型在科学应用中的效率和准确性。

排序理由 该集群包含两篇关于算子学习理论方面的arXiv预印本，包括误差分析和收敛速度。

在 arXiv cs.LG 阅读 →

AI 生成摘要 · Google Gemini · 来自 4 个来源。 我们如何撰写摘要 →

新研究详细介绍了基于核的算子学习，包含误差分析和物理信息扩展

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该集群包含两篇关于算子学习理论方面的arXiv预印本，包括误差分析和收敛速度。
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报道来源 [4]

  1. arXiv cs.LG TIER_1 English(EN) · R\"udiger Kempf ·

    基于核的算子学习：误差分析、预算分配及物理信息扩展

    arXiv:2607.06287v1 Announce Type: cross Abstract: We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconst…

  2. arXiv cs.LG TIER_1 English(EN) · Rüdiger Kempf ·

    基于核的算子学习：误差分析、预算分配及物理信息扩展

    We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from…

  3. Hugging Face Daily Papers TIER_1 English(EN) ·

    基于核的算子学习：误差分析、预算分配及物理信息扩展

    We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from…

  4. arXiv cs.LG TIER_1 English(EN) · Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen ·

    算子学习理论的简要介绍：收敛速度、统计极限和未解决的问题

    arXiv:2603.00819v2 Announce Type: replace-cross Abstract: This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomor…

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