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

Imagine you're designing a system to predict how structures behave under stress, like a bridge or a building. In many cases, a single input can lead to multiple valid outcomes, such as different ways a beam might buckle under load. Traditional models often assume a one-to-one relationship between inputs and outputs, which can lead to oversimplified predictions and missed critical behaviors. This limitation is particularly evident in complex physical systems where bifurcations occur, leading to multiple potential states from the same initial conditions. This is what's called a symmetry-breaking bifurcation, and it poses a challenge for existing deep learning methods that typically struggle to capture such complexities. To tackle this, a new framework called Bi-FORK has been developed. It learns to generate these one-to-many solution maps by effectively modeling the underlying dynamics of the system. By using techniques like latent flow matching and repulsion-guided sampling, Bi-FORK can explore and recover distinct solution branches in a single pass, maintaining coherence in both space and time. Compared to previous methods, Bi-FORK scales significantly better, handling high-dimensional systems with thousands of data points while accurately capturing the multimodal nature of solutions. For builders, this means you can now model complex physical phenomena more accurately, leading to better designs and predictions in engineering and materials science.

The approach addresses a largely unexplored area of deep learning related to bifurcations.

The evaluation on diverse physical systems demonstrates solid performance, though more extensive baselines could strengthen claims.