这篇论文提出的Bi-CFM方法，在混沌系统逆问题上比现有基线快上百倍，还能在守恒律上逼近真实值，值得AI建模爱好者细读。
Bi-CFM通过学习初始态与终态分布的双向映射，捕获混沌演化的随机性，缓解指数级误差累积。在Lorenz、Circuit和Lorenz 96系统上，Bi-CFM在5个分布级指标上超越基线，速度提升超两个数量级。针对行星动力学中的三体行星-行星散射问题，扩展的CBi-CFM守恒误差与真实值相当。在真实球状星团（约100亿年演化）观测中，该方法标志着长时序混沌逆问题的精度进步。
Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching
Modeling chaotic systems is crucial yet challenging. Inverse problems in chaotic dynamics, namely inferring initial conditions from final states, remain largely unsolved because of ill-posedness, non-uniqueness, instability, and potentially chaotic time-reverse dynamics. We address this open problem with Bidirectional Conditional Flow Matching (Bi-CFM), which learns bidirectional mappings between distributions of initial and final states to capture the stochasticity of chaotic evolution and mitigate exponential error accumulation over time. Furthermore, for systems with conservation laws, we extend it to Conservation-constrained Bi-CFM (CBi-CFM). Across the classic Lorenz, Circuit, and high-dimensional Lorenz 96 systems, Bi-CFM improves five distribution-level metrics over baselines while achieving a speedup of more than two orders of magnitude. In the three-body planet-planet scattering problem in planetary dynamics, CBi-CFM better respects conservation laws, with conservation errors comparable to those of the ground truth. Finally, on real observations of globular clusters, collisional million-body systems shaped by $\sim 10^{10}$ years (10 Gyr) of evolution, our method represents an advance in accuracy, establishing a scalable route to solving inverse problems of long-timescale real-world chaotic dynamics.