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

This project studies how to use Bi‑FORK, a generative‑modeling tool made for high‑dimensional systems that split into multiple branches, in water‑resources and environmental‑fluid work. Conventional numerical models often fail when a symmetry‑breaking bifurcation occurs—when the same boundary conditions can lead to several physically correct states. That situation breaks the usual one‑to‑one mapping assumption. Bi‑FORK handles this by matching latent flow fields and using repulsion‑guided sampling. The result is a set of full trajectories that stay consistent in space and time, even when they follow different solution branches. In water‑quality and environmental‑hydraulics, the method can reliably simulate: * multiple stable ecological states, * complex river splits, * phase‑separation effects in contaminant

transport. The research implements the generative model and tests its ability to recover multimodal solution structures in high‑dimensional problems, doing so more efficiently than traditional surrogate models. Simulation‑based validation shows how civil and environmental engineers can apply the approach to model nonlinear water systems with bifurcations. This should help improve risk assessment and decision‑making in water‑resource management.

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