Bi-FORK：高维分岔系统的生成建模
Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
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中文总结 AI 辅助
针对物理系统中对称破缺分岔的一对多解问题，提出Bi-FORK生成框架，通过潜在流匹配与斥力引导采样，在高维分岔系统上实现高效多模态解恢复，性能远超现有方法。
中文摘要 AI 辅助
分岔现象广泛存在于物理系统中，从结构屈曲到流体、气候动力学均有涉及，但在深度学习领域仍未得到充分探索。在对称破缺分岔处，单个输入对应多个同等有效的解，这违背了大多数学习型物理代理所基于的一对一假设。我们提出Bi-FORK，一种用于学习高维系统中此类一对多解映射的生成框架。Bi-FORK通过潜在流匹配生成完整轨迹，保持时空一致性，并采用斥力引导采样在单次摊销过程中恢复不同的解分支。我们在屈曲梁、机械超材料及Allen-Cahn相分离上对Bi-FORK进行评估，涵盖连续、离散和场值分岔，离散化点数高达260000。Bi-FORK可恢复多模态解结构，且规模远超现有方法数个数量级，为高维分岔物理系统的生成建模开辟了新途径。
英文摘要
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-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.
发表机构
- Department of Mathematics and Computer Science, Eindhoven University of Technology（埃因霍温理工大学数学与计算机科学系）
- Mistral（Mistral公司）
- DIFFER – Dutch Institute for Fundamental Energy Research（荷兰基础能源研究所（DIFFER））
机构由 AI 辅助整理，请以论文原文为准。
