{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T08:58:26Z","timestamp":1777107506973,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T00:00:00Z","timestamp":1740873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French Ministry of Higher Education and Research (MESR)","doi-asserted-by":"publisher","award":["ANR-R115RRO\/PAYPAFETA"],"award-info":[{"award-number":["ANR-R115RRO\/PAYPAFETA"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Fatigue has always been one of the major causes of structural failure, where repeated loading and unloading cycles reduce the fracture energy of the material, causing it to fail at stresses lower than its monotonic strength. However, predicting fatigue life is a highly challenging task and, in this context, the present study proposes a fundamentally new hybrid physics-informed and data-driven approach. Firstly, an energy-based fatigue model is developed to simulate the behavior of concrete under compressive cyclic fatigue loading. The data generated from these numerical simulations are then utilized to train machine learning (ML) models. The stress\u2013strain curve and S-N curve of concrete under compression, obtained from the energy-based model, are validated against experimental data. For the ML models, two different algorithms are used as follows: k-Nearest Neighbors (KNN) and Deep Neural Networks (DNN), where a total of 1962 data instances generated from numerical simulations are used for the training and testing of the ML models. Furthermore, the performance of the ML models is evaluated for out-of-range inputs, where the DNN model with three hidden layers (a complex model with 128, 64, and 32 neurons) provides the best predictions, with only a 0.6% overall error.<\/jats:p>","DOI":"10.3390\/computation13030061","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:04:49Z","timestamp":1740992689000},"page":"61","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Hybrid Physics-Informed and Data-Driven Approach for Predicting the Fatigue Life of Concrete Using an Energy-Based Fatigue Model and Machine Learning"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5128-0329","authenticated-orcid":false,"given":"Himanshu","family":"Rana","sequence":"first","affiliation":[{"name":"Laboratoire Roberval, Centre de Recherche Royallieu, University of Technology of Compi\u00e8gne-Alliance Sorbonne University, 60200 Compi\u00e8gne, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6502-0198","authenticated-orcid":false,"given":"Adnan","family":"Ibrahimbegovic","sequence":"additional","affiliation":[{"name":"Laboratoire Roberval, Centre de Recherche Royallieu, University of Technology of Compi\u00e8gne-Alliance Sorbonne University, 60200 Compi\u00e8gne, France"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,2]]},"reference":[{"key":"ref_1","unstructured":"Chudnovsky, A., and Sehanobish, K. 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