Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems
Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning.
Key points
- 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.
Sources (1)
- [1]Bi-FORK: Generative Modeling of High-Dimensional Bifurcating SystemsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 05:58 PM
Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning.
We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems.
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