从无时间标签的随机与量子系统数据中重建演化规律。
BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free data
- 用神经算子学习状态密度分布到演化参数的映射，设计了对顺序不敏感的架构。
- 在多种系统上成功恢复关键参数，包括3D蛋白折叠的冷冻电镜重构任务。
- 适合处理无时间戳观测数据的逆问题，尤其适用于生物物理建模。
我们研究在无时间标签设定下的随机与量子动力系统逆问题，仅能获取来自未知观察时间分布的无序密度快照。这些观测形成状态密度的分布，目标是从该分布中恢复底层演化算子的参数。我们将此问题建模为从分布到函数的神经算子学习，并提出BlinDNO，一种结合多尺度U-Net编码器与基于注意力的混合器的排列不变架构。在涵盖多种随机与量子系统的数值实验中，包括冷冻电镜环境下3D蛋白折叠机制的重建，结果表明BlinDNO能可靠地恢复控制参数，且持续优于现有神经逆算子基线方法。
原文摘要 · Abstract (English)
We study an inverse problem for stochastic and quantum dynamical systems in a time-label-free setting, where only unordered density snapshots sampled at unknown times drawn from an observation-time distribution are available. These observations induce a distribution over state densities, from which we seek to recover the parameters of the underlying evolution operator. We formulate this as learning a distribution-to-function neural operator and propose BlinDNO, a permutation-invariant architecture that integrates a multiscale U-Net encoder with an attention-based mixer. Numerical experiments on a wide range of stochastic and quantum systems, including a 3D protein-folding mechanism reconstruction problem in a cryo-EM setting, demonstrate that BlinDNO reliably recovers governing parameters and consistently outperforms existing neural inverse operator baselines.
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