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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12316 |
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| _version_ | 1866908656466919424 |
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| author | Zeng, Zhijun Chen, Junqing Shi, Zuoqiang |
| author_facet | Zeng, Zhijun Chen, Junqing Shi, Zuoqiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free data Zeng, Zhijun Chen, Junqing Shi, Zuoqiang Machine Learning Computational Engineering, Finance, and Science Dynamical Systems 35R30, 65M32, 68T07 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. |
| title | BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free data |
| topic | Machine Learning Computational Engineering, Finance, and Science Dynamical Systems 35R30, 65M32, 68T07 |
| url | https://arxiv.org/abs/2511.12316 |