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arXiv · 2610.12449

Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems

Anna Zimmel·Fleur Hendriks·Markus Holzleitner·Florian Sestak·Martin Weichselbaumer·Vlado Menkovski·Johannes Brandstetter
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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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Anna Zimmel, Fleur Hendriks, Markus Holzleitner, Florian Sestak, Martin Weichselbaumer, Vlado Menkovski, Johannes Brandstetter. 2026-10-08. Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems. https://arxiv.org/abs/2610.12449

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