发表机构
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对纯拉格朗日神经模拟器的空间瓶颈与时间漂移问题，提出混合拉格朗日-欧拉神经模拟器，通过自适应下采样与交叉注意力机制提升性能，实现了拉格朗日流体模拟的新精度与稳定性。
AI 中文摘要
纯拉格朗日神经模拟器具有几何灵活性和精确平流特性，非常适合建模移动域和自由表面。但由于缺乏固定全局参考系，存在两个严重局限：一是空间瓶颈，稳定梯度所需的密集粒子邻域被不加区分地应用，导致模型容量在均匀区域被浪费；二是快速时间漂移，由缺乏全局锚点的纯局部消息传递引发。受经典混合数值求解器启发，本文提出混合拉格朗日-欧拉神经模拟器，用欧拉表示增强拉格朗日动力学。为解决空间瓶颈，引入自适应下采样消除运动学冗余，保留粒子上的微观细节，同时将压缩特征聚合到欧拉节点以解析大规模动力学；为对抗时间漂移，采用交叉注意力机制查询欧拉特征，利用固定网格作为稳定空间锚点，在每个时间步校正轨迹偏差。综合实验表明，这种分层交叉注意力设计大幅抑制了误差累积，在拉格朗日流体模拟的精度和滚动稳定性方面达到了新的先进水平。
英文摘要
Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.
