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

2025-11-15

AI Summary

This work addresses the inverse problem for stochastic and quantum dynamical systems under missing time stamps: given only unordered snapshots of state density sampled from an unknown temporal distribution, the goal is to reconstruct parameters of the underlying evolution operator. To this end, we propose BlinDNO—the first permutation-invariant neural operator designed for unordered density distributions. It integrates a multi-scale U-Net encoder with an attention-driven mixing module to enable end-to-end mapping from density distributions to evolution operator parameters. The architecture inherently supports modeling temporal disorder and extracting multi-scale features. We validate BlinDNO across diverse stochastic and quantum systems, including cryo-EM-based reconstruction of protein conformational dynamics. Experimental results demonstrate substantial performance gains over existing neural inverse operators, establishing new state-of-the-art accuracy and robustness in time-agnostic dynamical inference.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Reconstructs dynamical systems from time-label-free density snapshots
• Learns evolution operator parameters from unordered state observations
• Solves inverse problems for stochastic and quantum systems

Innovation

• Uses permutation-invariant neural operator architecture
• Integrates multiscale U-Net encoder with attention
• Learns distribution-to-function mapping from unordered snapshots