[论文] Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems

论文概要

研究领域: ML 作者: Anna Zimmel, Fleur Hendriks, Markus Holzleitner, Florian Sestak, Martin Weichselbaumer, Vlado Menkovski, Johannes Brandstetter 发布时间: 2026-10-08 arXiv: 2610.12449

中文摘要

分叉现象在物理系统中无处不在——从结构屈曲到流体和气候动力学——但在深度学习中仍未得到充分探索。在对称性破缺分叉点，单一输入对应多个同等有效的解，违反了大多数学习物理替代模型所基于的一对一假设。我们提出 Bi-FORK，一个在高维系统中学习这些一对多解映射的生成框架。Bi-FORK 通过隐空间流匹配生成完整轨迹，保持时空连贯性，并使用排斥引导采样在单次摊销推理中恢复不同的解分支。我们在屈曲梁、机械超材料和 Allen-Cahn 相分离上评估 Bi-FORK，覆盖连续、离散和场值分叉，离散化规模高达 26 万点。Bi-FORK 在恢复多峰解结构的同时，将规模扩展超出先前方法数个数量级，为生成式建模打开了高维分叉物理系统的大门。

原文摘要

Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-val...

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