Bi-FORK：用生成模型学习高维分岔系统的多解映射
Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
一篇挺有意思的论文，教深度学习处理屈曲、相分离这类一对多解的分岔问题，单次推理就能出多个解分支，物理仿真方向的朋友可以看看。
arXiv 论文提出 Bi-FORK，一个针对对称破缺分岔系统的生成式建模框架。它通过 latent flow matching 生成完整轨迹，并用 repulsion-guided sampling 在单次 amortized pass 中恢复多个解分支，打破了传统物理代理模型的一对一映射假设。实验覆盖屈曲梁、机械超材料和 Allen-Cahn 相分离，涵盖连续、离散和场值型分岔，网格规模最高达 260,000 个离散点。相比此前方法，Bi-FORK 在多模态解结构恢复上扩展了几个数量级。
Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
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.
