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.
Keywords
Publication details
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Cite this article
APA 7
Zimmel, A., Hendriks, F., Holzleitner, M., Sestak, F., Weichselbaumer, M., Menkovski, V., & Brandstetter, J. (2026). Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems. https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems
MLA 9
Zimmel, Anna, et al. "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems." https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems.
Chicago (author–date)
Zimmel, Anna, Fleur Hendriks, Markus Holzleitner, Florian Sestak, Martin Weichselbaumer, Vlado Menkovski, and Johannes Brandstetter. 2026. "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems." https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems.
Harvard
Zimmel, A., Hendriks, F., Holzleitner, M., Sestak, F., Weichselbaumer, M., Menkovski, V. and Brandstetter, J. (2026) 'Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems', Available at: https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems.
Vancouver
Zimmel A, Hendriks F, Holzleitner M, Sestak F, Weichselbaumer M, Menkovski V, et al. Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems. https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems
IEEE
A. Zimmel, F. Hendriks, M. Holzleitner, F. Sestak, M. Weichselbaumer, V. Menkovski, and J. Brandstetter, "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems," https://omanscience.com/en/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems.