Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
Bi-FORK learns one-to-many bifurcation maps with latent flow matching and repulsion-guided sampling.
Bi-FORK is a generative framework for high-dimensional systems in which one input has multiple valid solutions at a symmetry-breaking bifurcation. It produces space-time-coherent trajectories with latent flow matching and uses repulsion-guided sampling to recover distinct branches in one amortized pass. Evaluations cover buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, with discretizations up to 260,000 points. The method recovers multimodal structure while scaling several orders of magnitude beyond prior surrogates.
- Learns one-to-many maps that standard physical surrogates cannot represent.
- Uses latent flow matching plus repulsion-guided branch sampling.
- Tested on beams, metamaterials, and Allen-Cahn fields up to 260,000 points.
- Scales several orders of magnitude beyond earlier bifurcation models.
From the original article
1 min read at arxiv.orgBifurcations 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.
By Anna Zimmel · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.