{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:13:46Z","timestamp":1750220026247,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>The majority of computer algebra systems (CAS) support symbolic integration using a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present a hybrid (symbolic-numeric) method to calculate the indefinite integrals of univariate expressions. Our method is broadly similar to the Risch-Norman algorithm. The primary motivation for this work is to add symbolic integration functionality to a modern CAS (the symbolic manipulation packages of SciML, the Scientific Machine Learning ecosystem of the Julia programming language), which is designed for numerical and machine learning applications. The symbolic part of our method is based on the combination of candidate terms generation (ansatz generation using a methodology borrowed from the Homotopy operators theory) combined with rule-based expression transformations provided by the underlying CAS. The numeric part uses sparse regression, a component of the Sparse Identification of Nonlinear Dynamics (SINDy) technique, to find the coefficients of the candidate terms. We show that this system can solve a large variety of common integration problems using only a few dozen basic integration rules.<\/jats:p>","DOI":"10.1145\/3572867.3572882","type":"journal-article","created":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:37:32Z","timestamp":1669250252000},"page":"84-87","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Symbolic-numeric integration of univariate expressions based on sparse regression"],"prefix":"10.1145","volume":"56","author":[{"given":"Shahriar","family":"Iravanian","sequence":"first","affiliation":[{"name":"Emory University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carl Julius","family":"Martensen","sequence":"additional","affiliation":[{"name":"Otto-von-Guericke University, Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Cheli","sequence":"additional","affiliation":[{"name":"University of Pisa, Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shashi","family":"Gowda","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anand","family":"Jain","sequence":"additional","affiliation":[{"name":"Julia Computing"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingbo","family":"Ma","sequence":"additional","affiliation":[{"name":"Julia Computing"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Rackauckas","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1517384113"},{"key":"e_1_2_1_2_1","volume-title":"Automated code optimization with e-graphs","author":"Cheli A.","year":"2021","unstructured":"Cheli , A. , and Rackauckas , C . Automated code optimization with e-graphs , 2021 . Cheli, A., and Rackauckas, C. Automated code optimization with e-graphs, 2021."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2009.08.032"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/74540.74567"},{"key":"e_1_2_1_5_1","unstructured":"Martensen J. Rackauckas C. etal Datadrivendiffeq.jl July 2021.  Martensen J. Rackauckas C. et al. Datadrivendiffeq.jl July 2021."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572882","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3572867.3572882","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:51:38Z","timestamp":1750182698000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572882"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1145\/3572867.3572882"],"URL":"https:\/\/doi.org\/10.1145\/3572867.3572882","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2022,6]]},"assertion":[{"value":"2022-11-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}