{"ID":2841396,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.12316","arxiv_id":"2511.12316","title":"BlinDNO: A Distributional Neural Operator for Dynamical System Reconstruction from Time-Label-Free 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.","short_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 t...","url_abs":"https://arxiv.org/abs/2511.12316","url_pdf":"https://arxiv.org/pdf/2511.12316v1","authors":"[\"Zhijun Zeng\",\"Junqing Chen\",\"Zuoqiang Shi\"]","published":"2025-11-15T18:15:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\",\"math.DS\"]","methods":"[]","has_code":false}