用于随机流动力学的拉格朗日椭球诊断：变形粒子云的源--汇建模
人工智能
2026-05-28 v1 软件工程
摘要
我们提出Lowner-John变形云方案作为不可压缩随机流动力学的拉格朗日诊断工具，适用于有惯性范围的情形。释放一个满载体积的粒子云于紫外尺度，并在每个时刻由两个对象概括：其最小包围椭球的惯性张量以及在该椭球上 coarse-grained的速度梯度。我们在二维各向同性不可压缩高斯-Holder有限时间相关速度场上进行测试，采用Kolmogorov指数生成，利用Ornstein-Uhlenbeck傅里叶模式。结果显示，椭球长宽比呈现较大波动但统计饱和，感知梯度 exhibits明显尺度依赖性，张量层面的应变-涡旋平衡约为正态分布。随后我们将云训练建模简化为基于物理的生成器识别。在描述尺度、长宽比、应变幅值、涡旋及应变-椭球对齐的内在变量中，长宽比动力学分解为对齐应变源和Lowner-John残差。最终的开放盒闭合模型将应变和涡旋建模为尺度依赖的随机驱动，代表对齐方式为平稳von-Mises偏置，并通过尺度相关的仿射反馈闭合残差。因此，观察到的长宽比饱和不仅是拟合而是解释为持续性应变对齐与包围椭球的几何松弛之间的平衡。该构建为从粒子云数据到可解释的有限维随机动力学提供了一种可携带的路径，适用于未来的湍流流动应用。
引用
@article{arxiv.2605.27605,
title = {Laguna M.1/XS.2 Technical Report},
author = {Julien Abadji and Marah Abdin and Connor Adams and Eric Alcaide and Mustafa Altun and Michele Artoni and Junze Bao and Uday Barar and Vassilis Bekiaris and Arkadii Bessonov and Benjamin Bütikofer and Jonathan Chang and Yen-Chun Chen and Dmitry Chernenkov and Yang Chi and Filippos Christianos and Fenia Christopoulou and Razvan-Andrei Ciocoiu and Tzachi Cohen and Yohann Coppel and Dmitrii Emelianenko and Brandon Fergerson and Brian Fitzgerald and Matthias Gallé and Alex Golonzovskyi and George Grigorev and Yiyang Hao and Christian Hensel and Jan Huenermann and Ye Ji and Sarthak Joshi and Eiso Kant and Kabir Khandpur and Seonghyeon Kim and Vladimir Kirichenko and Umut Kocasarac and Ilya Kochik and Ivan Komarov and Chaerin Kong and Anurag Koul and François-Joseph Lacroix and Sergei Laktionov and Waren Long and Quentin Malartic and Vadim Markovtsev and Afonso Marques and Robert McHardy and Carlos Mocholí and Dmitry Monakhov and Adam Morris and Martin Muller and Christian Mürtz and Robin Nabel and Thien Nguyen and Rok Novosel and Szymon Ozog and Aalhad Patankar and Aleksei Petrov and Alexandre Piché and Arthur Pignet and Teodor Poncu and Phil Potter and Alexander Rakowski and Pierre-Yves Ritschard and Jay Roberts and Joe Rowell and Piotr Sarna and Pierre-André Savalle and Uladzislau Sazanovich and Nikita Shapovalov and Arsenii Shevchenko and Mikhail Shilkov and Andrei Sokol and Mohamed Soliman and Jack Stephenson and Victor Storchan and Dragos-Constantin Tantaru and Artem Tyurin and Adrian Wälchli and Pengming Wang and Jianxiao Yang and Renat Zayashnikov and Alexander Zelenka Martin and Nikolay Zinov and Caroline Bercier and José Caldeira and Margarida Garcia and Tom George and Kabeer Gharzai and Glenn Hitchcock and Carson Klingenberg and Ivo Pinto and Varun Randery and Noah Smith and Arina Sugako and Jason Warner},
journal= {arXiv preprint arXiv:2605.27605},
year = {2026}
}
备注
Technical report to models released here: https://poolside.ai/blog/introducing-laguna-xs2-m1