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A model is a polynomial function of a space\u2013time signal designed to well-approximate solutions to partial differential equations (PDEs), even in low regularity regimes. Models can be seen as natural multi-dimensional generalisations of signatures of paths; our work therefore aims to extend the recent use of signatures in data science beyond the context of time-ordered data. We provide a flexible definition of a model feature vector associated to a space\u2013time signal, along with two algorithms which illustrate ways in which these features can be combined with linear regression. We apply these algorithms in several numerical experiments designed to learn solutions to PDEs with a given forcing and boundary data. Our experiments include semi-linear parabolic and wave equations with forcing, and Burgers\u2019 equation with no forcing. We find an advantage in favour of our algorithms when compared to several alternative methods. Additionally, in the experiment with Burgers\u2019 equation, we find non-trivial predictive power when noise is added to the observations.<\/jats:p>","DOI":"10.1007\/s10915-023-02401-4","type":"journal-article","created":{"date-parts":[[2023,11,23]],"date-time":"2023-11-23T09:02:30Z","timestamp":1700730150000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Feature Engineering with Regularity Structures"],"prefix":"10.1007","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5630-9694","authenticated-orcid":false,"given":"Ilya","family":"Chevyrev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andris","family":"Gerasimovi\u010ds","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hendrik","family":"Weber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,11,23]]},"reference":[{"key":"2401_CR1","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1038\/s41398-018-0334-0","volume":"8","author":"IP Arribas","year":"2018","unstructured":"Arribas, I.P., Goodwin, G.M., Geddes, J.R., Lyons, T., Saunders, K.E.A.: A signature-based machine learning model for distinguishing bipolar disorder and borderline personality disorder. 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