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Bi-FORK addresses a critical gap in deep learning by enabling generative models to handle high-dimensional systems with symmetry-breaking bifurcations, where traditional one-to-one mappings fail. By utilizing latent flow matching and repulsion-guided sampling, the framework successfully recovers distinct solution branches for complex physical phenomena like buckling beams and phase separation at unprecedented scales. This advancement expands the applicability of AI-driven scientific discovery to dynamic systems previously considered intractable for standard surrogate modeling.
Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
arXiv:2610.12449v1 Announce Type: cross 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph)
arXiv:2610.12449 [cs.LG]
(or arXiv:2610.12449v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.12449 arXiv-issued DOI via DataCite (pending registration)
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