BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free data

TL;DR

This paper introduces BlinDNO, a neural operator designed to reconstruct dynamical system parameters from unordered, time-label-free density data, demonstrating superior performance on stochastic and quantum systems including cryo-EM protein folding.

Contribution

BlinDNO is a novel permutation-invariant neural operator architecture that effectively learns from unordered density snapshots to recover system parameters.

Findings

BlinDNO accurately recovers parameters across diverse stochastic and quantum systems.

It outperforms existing neural inverse operator methods in experiments.

Successful application to cryo-EM protein folding data.

Abstract

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.