自适应交互图用于粒子模拟
Adaptive Interaction Graphs for Particle Simulation
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出自适应交互图方法 AdaptGNS，通过联合训练的方差头动态调整粒子邻域，在 WaterDrop 上实现严格 Pareto 改进，并揭示不确定性集中在复杂区域。
AI中文摘要：
基于图神经网络的 learned 粒子模拟器在单步精度上表现强劲，但在长时程预测中误差会累积。一个尚未充分探索的变量是交互图：现有方法通过 k 最近邻或静态半径规则固定其拓扑结构，而不考虑局部模型置信度。我们提出使该图具有自适应性：一个逐粒子方差头，与加速度头在异方差高斯负对数似然损失下联合训练，驱动一个轨迹，其中高不确定性粒子获得扩展的邻域。这几乎不增加推理成本，因为利用了上一步的不确定性估计。一个关键发现是，方差头学习到了有意义的 uncertainty 概念：高方差粒子集中在复杂区域附近，如飞溅区或自由表面。当此信号驱动图拓扑时，所得到的 AdaptGNS 模拟器在 WaterDrop 上实现了严格的 Pareto 改进，在 Sand 上获得了适度提升。鉴于模型在 WaterDrop 上的更强性能，我们假设自适应图在复杂度集中于空间时最为有用。我们的代码可在该 https URL 找到。
英文摘要：
Learned particle simulators based on graph neural networks achieve strong one-step accuracy, but errors compound over long horizons. An underexplored variable is the interaction graph: existing methods fix its topology via k-nearest neighbors or a static radius rule, regardless of local model confidence. We propose making this graph adaptive: a per-particle variance head, trained jointly with the acceleration head under a heteroscedastic Gaussian NLL loss, drives a trajectory in which high-uncertainty particles receive an expanded neighborhood. This is done at little extra inference cost by using the previous step's uncertainty estimate. A key discovery is that the variance head learns a meaningful notion of uncertainty: high-variance particles concentrate near complex regions, such as splash zones or free surfaces. When this signal drives graph topology, the resulting AdaptGNS simulator achieves a strict Pareto improvement on WaterDrop and a modest gain on Sand. Given the model's stronger performance on WaterDrop, we hypothesize that adaptive graphs are most useful when complexity is concentrated in space. Our code can be found at https://github.com/aidenzhou8/AdaptGNS.
