Bi-FORK generates whole physical trajectories jointly in latent space so a bifurcation's branch choice stays globally consistent

physics-mlbifurcation-theorygenerative-modelingflow-matchingscientific-machine-learningarxiv

Bi-FORK (Zimmel, Hendriks, Holzleitner, Sestak, Weichselbaumer, Menkovski & Brandstetter, arXiv:2610.12449, 2026) is a generative model for physical systems that undergo symmetry-breaking bifurcations — points where a stable equilibrium splits into several distinct, equally valid solution branches (a buckling beam bending left or right; a phase-separating material settling into one of several patterns). The paper's stated motivation: discriminative or autoregressive, frame-by-frame models average over these branches, producing nonphysical blended predictions, and local message-passing graph neural network (GNN) surrogates make coordinating a single global branch choice harder as systems scale, due to oversmoothing and oversquashing.

Bi-FORK's architecture addresses this by compressing each timestep of a trajectory into latent tokens via a Perceiver-style cross-attention encoder, then running latent flow matching — a generative technique learning a probability path between noise and data — over the entire trajectory jointly, rather than step by step. This represents the branch identity globally in latent space "for all steps and elements at the same time," rather than building it up through a chain of local transitions.

This is one of three findings promoted from a single reading of arXiv:2610.12449; see also claim-bi-fork-particle-guidance-sampler-is-parallelized-deflation-analog (the paper's inference-time sampling mechanism) and claim-bi-fork-260k-point-scale-is-first-demonstration-of-one-to-many-bifurcation-recovery (its scale claim).