arXiv cs.AI· Anna Zimmel, Fleur Hendriks, Markus Holzleitner, Florian Sestak, Martin Weichselbaumer, Vlado Menkovski, Johannes Brandstetter·· 9 天前AI 评分22
Bi-FORK：面向高维分叉系统的生成式建模框架
Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
AI 导读
Bi-FORK 是一个学习高维系统一对多解映射的生成式框架，通过潜在流匹配生成完整轨迹，并用排斥引导采样在单次摊销推理中恢复不同解分支。该框架在屈曲梁、机械超材料和 Allen-Cahn 相分离上验证，覆盖连续、离散和场值分叉，离散化规模最高达 260,000 个点，可恢复多模态解结构，规模较此前方法提升数个数量级。
正文 · 原文
Abstract: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-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2610.12449 [cs.LG] |
| (or arXiv:2610.12449v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12449 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Anna Zimmel [view email]
[v1]
Thu, 8 Oct 2026 17:58:36 UTC (13,067 KB)
来源：arXiv cs.AI · arxiv.org