Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
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.
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BibTeX
@misc{zimmel2026bifork,
title = {{Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems}},
author = {Anna Zimmel and Fleur Hendriks and Markus Holzleitner and Florian Sestak and Martin Weichselbaumer and Vlado Menkovski and Johannes Brandstetter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12449},
eprint = {2610.12449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
AU - Anna Zimmel
AU - Fleur Hendriks
AU - Markus Holzleitner
AU - Florian Sestak
AU - Martin Weichselbaumer
AU - Vlado Menkovski
AU - Johannes Brandstetter
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12449
UR - https://arxiv.org/abs/2610.12449
AB - 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.
ER -