The Bi-FORK model generated every known branch of a simulated buckling material’s response in 74% of test setups with two possible outcomes and 48% with four, according to an Oct. 8 preprint. When one physical setup can produce several stable shapes, a predictor that averages them can return a shape the material would never take.
The authors tested Bi-FORK on simulated buckling beams, patterned mechanical metamaterials, and phase separation, in which a mixture separates into patterns.
Instead of predicting one time step at a time, Bi-FORK compresses a system’s changing state into a smaller representation and generates a complete possible path. During sampling, a repulsion step pushes generated paths apart so they can represent different branches. The authors designed whole-path generation to keep one branch choice consistent across all points and times, rather than letting it switch halfway through a prediction.
In the metamaterial tests, the model generated 16 paths for each setup. “Full coverage” meant that valid generated paths included every known outcome. Bi-FORK achieved full coverage in 74% ± 1.0% of two-outcome setups and 48% ± 3.7% of four-outcome setups; the paper’s simpler deformation-only baseline covered none. The ± values are standard deviations across five test seeds. Without the repulsion step, coverage fell to 38% ± 0.9% and 13% ± 3.4%. The model’s average error against the nearest known outcome also rose slightly, from 0.016 without repulsion to 0.018 with it, illustrating the trade-off between diversity and precision.
The results come from three numerical simulations, not tests on physical materials. The largest simulations represented systems with up to 260,000 spatial points. The authors report that existing stochastic methods could not handle that scale, so they compared Bi-FORK there with the deformation-only baseline and their own model variants.
Sources
- Zimmel et al., “Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems,” arXiv (submitted Oct. 8, 2026)
- Full paper, including the metamaterial coverage definition and Table 12
Image credit: Figure 2 from Zimmel and colleagues’ Bi-FORK paper, CC BY 4.0.