注意力即所需（以避免虚假振荡）
Attention Is All You Need (to Avoid Spurious Oscillations)
- Kyungpook National University（庆北国立大学）
- University of Virginia（弗吉尼亚大学）
- University of Iowa（爱荷华大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出一种基于CFL条件注意力通量的守恒有限体积格式，实现大步长下激波的无振荡输运，并通过Burgers与浅水方程验证其有效性与局限性。
AI中文摘要：
注意力能否在一次更新中将激波移动穿过多个网格单元而不破坏它？我们开发了一种守恒的、固定网格的有限体积格式，其中由CFL条件约束的注意力通量根据当前时间步所需的输运来选择上游信息。一维无粘Burgers输运被用作核心机制测试：相同的学习通量在传统的小步长范围内保持可靠，并且在时间步长增大四倍的情况下，每步仅使用一个阶段即可保持尖锐激波。我们同时包含了标准五阶WENO格式结合三阶强稳定性保持龙格-库塔时间积分（WENO-5+SSP-RK3）作为对照，并与受控的前向欧拉比较，以区分通量选择与时间积分的作用。学习的注意力随局部输运范围向上游移动，并在激波附近变得更加具有选择性；推理时的干预和重新训练的消融实验表明，输运尺度信息和状态依赖的选择对性能有直接贡献。随后，二维方向性标量Burgers输运和一维浅水系统测试了守恒尺度选择原理是否能超越原始标量设置进行迁移。结果支持注意力作为一种可学习的、用于守恒大步长激波输运的信息模板，同时指出现有局限为有限的候选范围和依赖问题的鲁棒性。
英文摘要：
Can attention move a shock across several cells in one update without breaking it? We develop a conservative, fixed grid finite-volume scheme in which a CFL-conditioned attention flux selects upstream information according to the transport required by the current time step. One-dimensional inviscid Burgers transport is used as the central mechanism test: the same learned flux remains reliable in the conventional small-step regime and, with a time step four times larger, preserves sharp shocks while using one stage per update. A standard fifth-order WENO scheme with third-order strong-stability-preserving Runge-Kutta time integration (WENO-5+SSP-RK3) is included alongside controlled Forward Euler comparisons to separate flux selection from time integration. The learned attention shifts upstream with the local transport reach and becomes more selective near shocks; inference-time interventions and retrained ablations show that transport-scale information and state-dependent selection contribute directly to performance. Directional two-dimensional scalar Burgers transport and the one-dimensional shallow-water system then test whether the conservation-scale-selection principle transfers beyond the original scalar setting. The results support attention as a learnable information stencil for conservative large-step shock transport, while identifying finite candidate reach and problem-dependent robustness as the present limits.
