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To establish the interactions between genes or proteins and understand the intrinsic mechanisms of biological systems have become an urgent need and study hotspot.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In order to forecast gene expression data and identify more accurate gene regulatory network, complex-valued version of ordinary differential equation (CVODE) is proposed in this paper. In order to optimize CVODE model, a complex-valued hybrid evolutionary method based on Grammar-guided genetic programming and complex-valued firefly algorithm is presented.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>When tested on three real gene expression datasets from<jats:italic>E.<\/jats:italic><jats:italic>coli<\/jats:italic>and Human Cell, the experiment results suggest that CVODE model could improve 20\u201350% prediction accuracy of gene expression data, which could also infer more true-positive regulatory relationships and less false-positive regulations than ordinary differential equation.<\/jats:p><\/jats:sec>","DOI":"10.1186\/s12859-021-04367-2","type":"journal-article","created":{"date-parts":[[2021,9,20]],"date-time":"2021-09-20T09:09:18Z","timestamp":1632128958000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Reverse engineering gene regulatory network based on complex-valued ordinary differential equation model"],"prefix":"10.1186","volume":"22","author":[{"given":"Bin","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1471-5432","authenticated-orcid":false,"given":"Wenzheng","family":"Bao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haifeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuandong","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuehui","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuying","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,20]]},"reference":[{"issue":"9","key":"4367_CR1","doi-asserted-by":"publisher","first-page":"R92","DOI":"10.1186\/gb-2009-10-9-r92","volume":"10","author":"S Marcel","year":"2009","unstructured":"Marcel S, Ramon MMJ, Panagiota M, Wittbrodt B, Wittbrodt J. 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