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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.22328 |
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| _version_ | 1866910274713288704 |
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| author | Muscarnera, Luca Estévez, Silas Ruhrberg Holt, Samuel Saveliev, Evgeny van der Schaar, Mihaela |
| author_facet | Muscarnera, Luca Estévez, Silas Ruhrberg Holt, Samuel Saveliev, Evgeny van der Schaar, Mihaela |
| contents | Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories. Instead, measurements are often partial, noisy, and heterogeneous, providing fragmented views of latent dynamical states. We introduce MAAT (Model Aware Approximation of Trajectories), a framework for knowledge-informed Kernel State Reconstruction in partially observed dynamical systems. MAAT formulates reconstruction in a reproducing kernel Hilbert space and incorporates heterogeneous observation operators together with semantic and structural priors, including non-negativity, conservation constraints, and domain-specific measurement models. This yields smooth, physically consistent state estimates with analytic time derivatives, providing a principled interface between fragmented measurements and downstream mechanistic discovery methods such as symbolic regression. Across nine scientific benchmarks, multiple noise regimes, and a real-world COVID-19 dataset, MAAT substantially reduces trajectory and derivative reconstruction error relative to strong baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations Muscarnera, Luca Estévez, Silas Ruhrberg Holt, Samuel Saveliev, Evgeny van der Schaar, Mihaela Machine Learning Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories. Instead, measurements are often partial, noisy, and heterogeneous, providing fragmented views of latent dynamical states. We introduce MAAT (Model Aware Approximation of Trajectories), a framework for knowledge-informed Kernel State Reconstruction in partially observed dynamical systems. MAAT formulates reconstruction in a reproducing kernel Hilbert space and incorporates heterogeneous observation operators together with semantic and structural priors, including non-negativity, conservation constraints, and domain-specific measurement models. This yields smooth, physically consistent state estimates with analytic time derivatives, providing a principled interface between fragmented measurements and downstream mechanistic discovery methods such as symbolic regression. Across nine scientific benchmarks, multiple noise regimes, and a real-world COVID-19 dataset, MAAT substantially reduces trajectory and derivative reconstruction error relative to strong baselines. |
| title | Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.22328 |