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 hi...
| Authors | Peiyan Hu, Jian Zhang, Jiashu Pan et al. |
|---|---|
| Primary category | cs.AI |
| Published | 23 June 2026 |
| Last updated at source | 23 June 2026 |
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