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Frequently, sensors have extremely sparse coverage and low-resource computing capacity for measuring highly nonlinear phenomena. While numerical simulations can model some of these phenomena using partial differential equations, the reconstruction problem is ill-posed. Data-driven-strategies provide crucial disambiguation, but these suffer in cases with small amounts of data, and struggle to handle large domains. Here we present the Senseiver, an attention-based framework that excels in reconstructing complex spatial fields from few observations with low overhead. The Senseiver reconstructs <jats:italic>n<\/jats:italic>-dimensional fields by encoding arbitrarily sized sparse sets of inputs into a latent space using cross-attention, producing uniform-sized outputs regardless of the number of observations. This allows efficient inference by decoding only a sparse set of output observations, while a dense set of observations is needed to train. This framework enables training of data with complex boundary conditions and extremely large fine-scale simulations. We build on the Perceiver IO by enabling training models with fewer parameters, which facilitates field deployment, and a training framework that allows a flexible number of sensors as input, which is critical for real-world applications. We show that the Senseiver advances the state-of-the-art of field reconstruction in many applications.<\/jats:p>","DOI":"10.1038\/s42256-023-00746-x","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T17:04:04Z","timestamp":1699290244000},"page":"1317-1325","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":79,"title":["Development of the Senseiver for efficient field reconstruction from sparse observations"],"prefix":"10.1038","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2404-3975","authenticated-orcid":false,"given":"Javier E.","family":"Santos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zachary R.","family":"Fox","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arvind","family":"Mohan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0432-3088","authenticated-orcid":false,"given":"Daniel","family":"O\u2019Malley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hari","family":"Viswanathan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicholas","family":"Lubbers","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"key":"746_CR1","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1109\/MGRS.2015.2441912","volume":"3","author":"H Shen","year":"2015","unstructured":"Shen, H. et al. 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