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This study develops a physics-informed neural network that overcomes limitations of purely data-driven approaches by incorporating physical consistency and loading-path characteristics. The model uses a parallel CNN-LSTM architecture for spatial–temporal feature extraction and multi-head attention to fuse features with material properties. Physical laws are embedded through the loss function, yielding stronger generalization and parameter efficiency. Interpretability is provided via SHAP and Grad-CAM, showing that peak shear stresses and rapid stress-change rates drive predictions and that tensile strength is most influential.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/a-physics-informed-neural-network-for-high-accuracy-multiaxial-fatigue-life-prediction-of-aluminum-alloys-with-mechanical-interpretation/628679/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/a-physics-informed-neural-network-for-high-accuracy-multiaxial-fatigue-life-prediction-of-aluminum-alloys-with-mechanical-interpretation/628679.png","ImageObject",300,407,{"name":92,"@type":93},"Aria Callaghan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-10-21",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper address in multiaxial fatigue life prediction?","Question",{"text":112,"@type":113},"It addresses accurate prediction of multiaxial fatigue life for aluminum alloys under intricate, non-proportional loading paths, which data-driven methods struggle to capture while maintaining physical consistency.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed physics-informed neural network incorporate physical interpretation?",{"text":117,"@type":113},"It embeds physical laws into the training loss function, linking fatigue life behavior to material mechanics (e.g., higher tensile and yield strengths improving life), while using attention-based fusion and CNN-LSTM feature extraction.",{"name":119,"@type":110,"acceptedAnswer":120},"What methods are used for model interpretability and what do they reveal?",{"text":121,"@type":113},"SHAP and Grad-CAM are used to quantify feature contributions and visualize critical path regions, revealing that peak shear stresses and rapid stress-change rates dominate predictions, with tensile strength most critical among material properties.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},628679,1792617871,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Fatigue & Fracture of Engineering Materials & Structures  \nORIGINAL ARTICLE  \nA Physics-Informed Neural Network for High-Accuracy Multiaxial-Fatigue Life Prediction of Aluminum Alloys With Mechanical Interpretation  \nYong-gui Chen  | Xin-hao Shu | Zheng-wei Fan | Shu-feng Zhang  \nNational Key Laboratory of Equipment State Sensing and Smart Support, College of Intelligence Science and Technology, National University of Defense Technology, Changsha, China  \nCorrespondence: Shu-feng Zhang ([sfzhang@nudt.edu.cn](sfzhang@nudt.edu.cn))  \nReceived: 30 December 2025 | Revised: 31 March 2026 | Accepted: 8 April 2026  \nKeywords: aluminum alloys | interpretability | multiaxial-fatigue life | physics-informed neural network  \nABSTRACT  \nAccurate prediction of multiaxial fatigue life is crucial for structural integrity. This study proposes a physics-informed neural network for multiaxial fatigue life prediction of aluminum alloys, addressing the limitations of purely data-driven methods in capturing loading path characteristics, while ensuring physical consistency. The model integrates a parallel CNN-LSTM architecture to extract spatial–temporal features from loading paths, while a multi-head attention mechanism fuses these with material properties. The physical laws (higher tensile and yield strengths enhance fatigue life) are embedded via loss function. Compared with other purely data-driven models, the proposed model achieves superior generalization (R2 = 0.873, with 97.3% of predictions within 3 times error band on the life prediction) and significant reduction in model parameters. Furthermore, SHAP and Grad-CAM provide interpretability by quantifying feature contributions and visualizing critical path regions. Analysis reveals peak shear stresses and rapid stress change rates dominate predictions, and tensile strength is the most critical factor among material properties.  \n1 | Introduction  \nAluminum alloys, with high strength-to-weight ratio, ductility, and favorable formability, have become indispensable in critical applications across aviation and aerospace [1, 2] . However, they are susceptible to multiaxial-fatigue failure under the intricate multiaxial alternating stresses caused by air current or other factors. This often leads to significant sudden accidentsand economic losses [3] . To address these challenges, significant research has focused on multiaxial-fatigue mechanisms, influencing factors, and life predictive modeling. For example, Seyda et al. [4] studied the behavior of small cracks in 6060-T6 aluminum alloy under multiaxial-fatigue loadings; Liu et al. [5] assessed the damage evolution process and failure mechanism of 2024-T351 aluminum alloy under multiaxial loading. Among these research fields, the development of multiaxial-fatigue life  \nprediction model has always been a research hotspot, yet remains a challenge due to the complexity of material behavior, loading history, etc.  \nEarly multiaxial-fatigue life prediction models primarily focused on the development of appropriate damage parameters (also known as fatigue criteria) and used experimental or theoretical methods to establish their nonlinear relationships with fatigue life [6, 7] . For instance, Wang et al. [8] proposed a multiaxialfatigue damage parameters including stress and strain, while Ince et al. [9] proposed a fatigue damage parameter formulated on the generalized strain energy, which incorporates an elastic shear term and a normal strain energy term to account for the effects of mean stress and non-proportional hardening. However, these empirical models face significant limitations in practical applications. Firstly, their robustness and generalizability are  \n© 2026 John Wiley & Sons Ltd.  \nFatigue & Fracture of Engineering Materials & Structures, 2026; 49:2945–2962 2945  \n[https://doi.org/10.1111/ffe.70297](https://doi.org/10.1111/ffe.70297)  \nSummary  \n1. A physics-informed neural network (PINN) was developed to predict the multiaxial fatigu","cbCaiame8dI5Ode4","https://ap.wps.com/l/cbCaiame8dI5Ode4","pdf",5094898,18,"English","# Introduction\n## Multiaxial fatigue challenges and need for robust modeling\n## Traditional fatigue criteria and their limitations\n## Data-driven machine learning approaches and the gap for multiaxial loading","[{\"question\":\"What problem does the paper address in multiaxial fatigue life prediction?\",\"answer\":\"It addresses accurate prediction of multiaxial fatigue life for aluminum alloys under intricate, non-proportional loading paths, which data-driven methods struggle to capture while maintaining physical consistency.\"},{\"question\":\"How does the proposed physics-informed neural network incorporate physical interpretation?\",\"answer\":\"It embeds physical laws into the training loss function, linking fatigue life behavior to material mechanics (e.g., higher tensile and yield strengths improving life), while using attention-based fusion and CNN-LSTM feature extraction.\"},{\"question\":\"What methods are used for model interpretability and what do they reveal?\",\"answer\":\"SHAP and Grad-CAM are used to quantify feature contributions and visualize critical path regions, revealing that peak shear stresses and rapid stress-change rates dominate predictions, with tensile strength most critical among material properties.\"}]","A Physics-Informed Neural Network for High-Accuracy Multiaxial-Fatigue Life Prediction of Aluminum Alloys With Mechanical Interpretation | PDF",45]