Bi-FORK: Generative Modeling for High-Dimensional Bifurcating Physical Systems
Bi-FORK：高維分歧物理系統的生成式建模框架
Standard physical surrogates rely on a one-to-one mapping assumption, which fails at physical bifurcations where a single input leads to multiple valid trajectories. Bi-FORK introduces a generative framework that models one-to-many solution maps in high-dimensional physical systems. By combining latent flow matching for spatiotemporal coherence with repulsion-guided sampling to capture distinct solution branches in a single amortized pass, Bi-FORK successfully handles discrete, continuous, and field-valued bifurcations across systems scaled up to 260,000 discretization points.
Key points
Solving One-to-Many Bifurcations
Overcomes the one-to-one mapping constraint of traditional surrogates to accurately capture multiple valid solutions at symmetry-breaking bifurcations.
Spatiotemporal Coherence via Latent Flow Matching
Generates complete physical trajectories via latent flow matching, ensuring spatial and temporal consistency across states.
Single-Pass Discovery with Repulsion Guidance
Uses repulsion-guided sampling to uncover distinct solution branches in a single amortized inference pass.
Unprecedented High-Dimensional Scalability
Scales several orders of magnitude beyond prior approaches, demonstrating efficacy on discretizations up to 260,000 points.
How it works
Why it matters
Physical systems frequently exhibit symmetry-breaking bifurcations where deterministic AI surrogates fail. Bi-FORK bridges this gap by enabling scalable, generative modeling of multi-modal physical trajectories. This opens new opportunities for designing mechanical metamaterials, assessing structural stability, and simulating complex dynamical field processes.
Who it affects
- AI Researcher
- AI Developer
- Enterprise Leader
How to use it
- 1Mechanical metamaterial and structural buckling analysis
- 2Phase separation and dynamical field simulation (e.g., Allen-Cahn equation)
Limitations & caveats
- Generative quality depends on the quality and stability of the latent space representation
- Extremely rare or complex bifurcation branches may require fine-tuning sampling guidance parameters
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