[
    {
        "id": "osp-14941",
        "type": "article-journal",
        "title": "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems",
        "author": [
            {
                "family": "Zimmel",
                "given": "Anna"
            },
            {
                "family": "Hendriks",
                "given": "Fleur"
            },
            {
                "family": "Holzleitner",
                "given": "Markus"
            },
            {
                "family": "Sestak",
                "given": "Florian"
            },
            {
                "family": "Weichselbaumer",
                "given": "Martin"
            },
            {
                "family": "Menkovski",
                "given": "Vlado"
            },
            {
                "family": "Brandstetter",
                "given": "Johannes"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/bi-fork-generative-modeling-of-high-dimensional-bifurcating-systems",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]