研究人员开发了一种新的学习预处理器McMg，用于求解异构亥姆霍兹方程，与经典方法相比，它显著减少了迭代次数和计算时间。该方法通过在每个粗节点上携带学习到的幅度、相位、方向和散射系数，而不是单一标量未知数，来保留未解析的局部波信息。模型展示了跨不同尺度和问题的泛化能力，性能优于现有的神经预处理器。 AI
影响 这项研究可能导致更有效的计算方法来解决复杂的物理问题，可能影响依赖模拟的领域。
排序理由 该集群包含多篇arXiv论文，详细介绍了计算方法和机器学习的新研究。
AI 生成摘要 · Google Gemini · 来自 5 个来源。 我们如何撰写摘要 →
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arXiv:2508.12270v3 Announce Type: replace Abstract: End-to-end deep learning has achieved impressive results but often relies on large labeled datasets, exhibits limited generalization to unseen scenarios, and incurs substantial computational cost. Classical optimization methods,…
arXiv:2606.30495v1 Announce Type: cross Abstract: Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and…
Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and propagation-direction information carried by osci…
arXiv:2605.08390v2 Announce Type: replace Abstract: Sequence prediction methods for linear dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows linearly with the hidden dimension of the underlying generative model. While many met…
arXiv:2602.10714v2 Announce Type: replace-cross Abstract: Preconditioning is a common method applied to modify Markov chain Monte Carlo algorithms with the goal of making them more efficient. In practice it is often extremely effective, even when the preconditioner is learned fro…