用双向流匹配解决混沌系统反演难题，高效精准推断初始状态。
Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching
- 提出双向条件流匹配，学习初态与终态间的双向映射。
- 在洛伦兹、电路等系统上提升五项分布指标，提速超百倍。
- 适用于守恒定律系统，适合长期演化的真实混沌场景建模。
建模混沌系统至关重要但极具挑战。混沌动力学中的逆问题——从终态推断初态——因病态性、非唯一性、不稳定性及可能的混沌时间反演而长期未解。本文提出双向条件流匹配（Bi-CFM），通过学习初态与终态分布间的双向映射，捕捉混沌演化中的随机性，缓解误差随时间指数累积问题。针对具有守恒律的系统，进一步提出守恒约束的Bi-CFM（CBi-CFM）。在经典洛伦兹系统、电路系统及高维洛伦兹96系统中，Bi-CFM在五项分布级指标上优于基线方法，且提速超过两个数量级。在行星动力学中的三体行星散射问题中，CBi-CFM更严格遵守守恒律，其守恒误差接近真实值。最后，在真实球状星团观测数据上，该方法处理了约10^10年（10 Gyr）演化形成的百万粒子碰撞系统，显著提升精度，为解决长时序真实混沌系统的逆问题提供了可扩展路径。
原文摘要 · Abstract (English)
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.
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