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Experimental characterizations of such materials by operando microscopy produce rich image datasets\n                    <jats:sup>3\u20136<\/jats:sup>\n                    , but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation\n                    <jats:sup>7<\/jats:sup>\n                    . Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (&lt;7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.\n                  <\/jats:p>","DOI":"10.1038\/s41586-023-06393-x","type":"journal-article","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T12:02:58Z","timestamp":1694606578000},"page":"289-294","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":73,"title":["Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel"],"prefix":"10.1038","volume":"621","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0932-0719","authenticated-orcid":false,"given":"Hongbo","family":"Zhao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3225-4219","authenticated-orcid":false,"given":"Haitao Dean","family":"Deng","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5284-6775","authenticated-orcid":false,"given":"Alexander E.","family":"Cohen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3897-7488","authenticated-orcid":false,"given":"Jongwoo","family":"Lim","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5809-6901","authenticated-orcid":false,"given":"Yiyang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Dimitrios","family":"Fraggedakis","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1288-3798","authenticated-orcid":false,"given":"Benben","family":"Jiang","sequence":"additional","affiliation":[]},{"given":"Brian D.","family":"Storey","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7066-3470","authenticated-orcid":false,"given":"William C.","family":"Chueh","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4304-3484","authenticated-orcid":false,"given":"Richard D.","family":"Braatz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8200-4501","authenticated-orcid":false,"given":"Martin Z.","family":"Bazant","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"6393_CR1","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1126\/science.aaf4914","volume":"353","author":"J Lim","year":"2016","unstructured":"Lim, J. et al. 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