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

Forum topic · 小凯 · 2026-10-10

Summary

Bi-FORK (arXiv:2610.12449) is a generative deep learning framework for modeling bifurcating physical systems, where a single input admits multiple equally valid solutions. Bifurcations, ubiquitous in structural buckling, fluid dynamics, and climate dynamics, violate the one-to-one input-output assumption of most learned physics surrogates. Bi-FORK generates complete trajectories via latent flow matching to preserve spatiotemporal coherence, and applies repulsion-guided sampling to recover distinct solution branches in a single amortized inference pass. The authors, including Anna Zimmel, Markus Holzleitner, Vlado Menkovski, and Johannes Brandstetter, evaluate the framework on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, covering continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers multimodal solution structures while scaling several orders of magnitude beyond prior methods, opening the door to generative modeling of high-dimensional bifurcating physical systems.

Overview

Field: Machine Learning Authors: Anna Zimmel, Fleur Hendriks, Markus Holzleitner, Florian Sestak, Martin Weichselbaumer, Vlado Menkovski, Johannes Brandstetter Published: 2026-10-08 arXiv: 2610.12449

Abstract (translated from Chinese summary)

Bifurcation phenomena are ubiquitous in physical systems — from structural buckling to fluid and climate dynamics — but remain largely unexplored in deep learning. At a symmetry-breaking bifurcation point, a single input corresponds to multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogate models.

The authors propose 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 spatiotemporal coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized inference pass.

Evaluation

Bi-FORK is evaluated on:

Buckling beams (continuous bifurcation)
Mechanical metamaterials (discrete bifurcation)
Allen-Cahn phase separation (field-valued bifurcation)

Discretization scales reach up to 260,000 points. Bi-FORK recovers multimodal solution structure while scaling several orders of magnitude beyond previous methods, opening the door to generative modeling of high-dimensional bifurcating physical systems.

Original Abstract (excerpt)

> 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...

Full paper: arXiv:2610.12449

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