BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free data
This addresses the challenge of inverse problems in dynamical systems for applications like cryo-EM, though it is incremental as it builds on neural operator methods.
The authors tackled the problem of reconstructing stochastic and quantum dynamical systems from unordered density snapshots with unknown sampling times, proposing BlinDNO, a distributional neural operator that reliably recovers governing parameters and outperforms existing baselines in numerical experiments, including a 3D protein-folding reconstruction.
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.