发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出WAMRViT，利用四叉树分词和3D旋转位置嵌入动态自适应网格，实现高效长时PDE预测，优于均匀网格基线。
AI 中文摘要
视觉Transformer（ViTs）的二次注意力代价迫使空间分辨率与滚动预测时长之间进行权衡，尤其是在细尺度偏微分方程（PDE）中，激波、反应前沿和材料界面占据域内小而演化的区域。传统神经替代模型也缺乏动态调整分辨率的机制。我们提出WAMRViT，一种视觉Transformer，它使用基于小波的细化准则将输入分词为平衡四叉树，通过3D旋转位置嵌入联合编码位置和细化级别，并在推理期间在单元空间重新网格化以实现稳定的长时滚动预测。多尺度变体将每个叶节点保留在其原生源分辨率，并让模型跨分辨率级别学习。与固定预算的自适应分词方法不同，WAMRViT不预设标记数量，并在自回归滚动过程中支持完全自适应的拓扑结构。据我们所知，它是首个原生分词多级自适应网格细化（AMR）数据的机器学习替代模型。在均匀网格基准上，均匀补丁WAMRViT在细粒度感兴趣区域VRMSE上优于细粒度补丁均匀ViT，同时使用显著更少的标记。多尺度变体在两个基准上实现了最低的第一步全字段RMSE和VRMSE，并在长时滚动中提高了滚动平均的全字段和细化区域精度。通过并行化重新网格化，其端到端滚动成本介于细粒度补丁和近似标记匹配的粗粒度补丁ViT之间。在一个复杂的AMR燃烧问题上，其最细特征无法由评估的均匀网格基线原生表示，WAMRViT直接操作自适应单元，并在匹配的Transformer容量下显著降低了最细级别误差。代码：此https URL
英文摘要
The quadratic attention cost of Vision Transformers (ViTs) forces a trade-off between spatial resolution and rollout horizon, particularly for fine-scale PDEs where shocks, reaction fronts, and material interfaces occupy small, evolving regions of the domain. Conventional neural surrogates also lack mechanisms to adapt resolution dynamically. We propose WAMRViT, a ViT that tokenizes inputs as balanced quadtrees using a wavelet-inspired refinement criterion, jointly encodes position and refinement level with 3D rotary positional embeddings, and regrids in cell space during inference for stable long-horizon rollouts. A multi-scale variant retains each leaf at its native source resolution and lets the model learn across resolution levels. Unlike fixed-budget adaptive-tokenization methods, WAMRViT imposes no predetermined token count and supports fully adaptive topology throughout autoregressive rollout. To our knowledge, it is the first machine-learning surrogate to natively tokenize multi-level Adaptive Mesh Refinement (AMR) data. On uniform-grid benchmarks, uniform-patch WAMRViT improves finest-level region-of-interest VRMSE over a finest-patch uniform ViT while using substantially fewer tokens. The multi-scale variant achieves the lowest first-step full-field RMSE and VRMSE on both benchmarks and improves rollout-averaged full-field and refined-region accuracy at long horizons. With parallelized regridding, its end-to-end rollout cost lies between finest-patch and approximately token-matched coarser-patch ViTs. On a complex AMR combustion problem whose finest features cannot be represented natively by the evaluated uniform-grid baselines, WAMRViT operates directly on adaptive cells and substantially reduces finest-level error at matched transformer capacity. Code: https://github.com/tonyzyl/wamrvit
