[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-455649-en":59,"doc-seo-455649-105":80},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":31},455649,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Practical sparse data-driven constitutive modeling via transfer learning in physics-encoded neural networks","Data-driven constitutive models can provide flexible alternatives to conventional plasticity-based models, especially when calibrated to satisfy fundamental mechanical principles and embedded into finite element method (FEM) solvers as physics-encoded neural networks (PeNNs). Calibration becomes difficult under limited data availability, so transfer learning is used. PeNNs are pre-trained with synthetic labeled data from traditional models, then fine-tuned using implicitly labeled information from high-fidelity experiments and validated via drained and undrained triaxial simulations.","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nOPEN  \nPractical sparse data-driven constitutive modeling via transfer learning in physics-encoded neural networks  \nZhihui Wang􀀍 & Roberto Cudmani  \nData-driven constitutive models, owing to their inherent flexibility, can outperform traditional plasticity-based models in certain aspects. When calibrating these models, ensuring adherence to fundamental mechanical principles allows the calibrated models, referred to as physics-encoded neural networks (PeNNs), to be effectively integrated into finite element method (FEM) software for boundary value problem simulations. However, calibration challenges arise when only limited data are available. Addressing this issue, this study employs transfer learning. Synthetic labeled data, derived from traditional constitutive models were used to pre-train PeNNs. Subsequently, these pre-trained PeNNs are fine-tuned using implicitly labeled data from high-fidelity experimental records. The finetuned models are integrated into FEM software as user materials to conduct extensive drained and undrained triaxial test simulations. An analysis of the simulation results highlights the impact of the available volume of experimental data, the quantity of synthetic data, and key configurations in the fine-tuning process, such as the architecture of the fine-tuning model, frozen parameters, and batch size. Results indicate that through robust PeNN models and meticulous modeling, transfer learning can establish a data-driven constitutive model with limited experimental records, achieving superior simulation performance compared to the synthetic model alone. This underscores the potential of combining cost-effective synthetic and experimental data to advance constitutive modeling.  \nKeywords Physics-encoded neural networks, Constitutive model, Soil mechanics, Hypoplasticity, Machine learning, Transfer learning  \nIn the field of Architecture, Engineering, and Construction, Computer-Aided Design facilitates precise geometric modeling, while Computer-Aided Engineering enables simulation-based analysis of mechanical performance1,2. Together, they support integrated design workflows, enhance decision-making and improve the efficiency and reliability of construction and engineering processes3. In this workflow, constitutive models provide critical support for simulating complex boundary value problems by effectively describing the stressstrain relationships observed in experiments4. They play a key role in various numerical algorithms such as finite element methods (FEM), finite difference methods, smoothed particle hydrodynamics, the material point method, and the particle finite element methods5–7. Due to the inherent complexity of geomaterials, it becomes necessary to introduce appropriate simplifications and assumptions8 to establish practical phenomenological constitutive models that enable reliable simulations. Over the years, these phenomenological constitutive models have undergone significant developments, evolving from simple linear elastic models, such as Hooke’s Law9, to models that reflect nonlinear elasticity, like the modified Duncan-Chang model10, and plastic constitutive models that account for irreversible deformations, such as the modified Mohr-Coulomb model11. These advancements have further extended to various models based on critical state soil mechanics12–14.  \nNatural geomaterials, with their complex mineral compositions and microstructures, present challenges in characterizing their mechanical behavior15. To more accurately simulate the stress-strain relationships observed under various conditions, traditional phenomenological plasticity models have increasingly incorporated additional material parameters and state variables16. The proliferation of these parameters inevitably raises issues related to parameter calibration and mutual interactions17. Particularly, certain state parameters are challenging to measure d","cbCainHz2q0axO1h","https://ap.wps.com/l/cbCainHz2q0axO1h","pdf",6355050,3,"English","en",105,"# Introduction\n## Constitutive modeling in AEC workflows\n## Limitations of traditional phenomenological models\n## AI-based constitutive modeling approaches","[{\"question\":\"What problem does the study address in physics-encoded neural networks calibration?\",\"answer\":\"It addresses calibration difficulty when only limited experimental data are available, which makes reliable physics-embedded training challenging.\"},{\"question\":\"How does the study use transfer learning in this framework?\",\"answer\":\"It pre-trains PeNNs on synthetic labeled data generated from traditional constitutive models, then fine-tunes them using implicitly labeled data derived from high-fidelity experimental records.\"},{\"question\":\"How are the resulting models evaluated?\",\"answer\":\"The fine-tuned PeNNs are integrated into FEM software as user material models and assessed through extensive drained and undrained triaxial test simulations, analyzing effects of data volume and fine-tuning configurations.\"}]","Practical sparse data-driven constitutive modeling via transfer learning in physics-encoded neural networks | PDF",1790743753,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":138,"head_meta":140,"extra_data":142,"updated_unix":143},"practical-sparse-data-driven-constitutive-modeling-via-transfer-learning-in-physics-encoded-neural-networks","",{"@graph":86,"@context":137},[87,100,120],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,98],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":40,"@type":93,"position":72},"https://docshare.wps.com/document/research-report/",{"item":99,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/practical-sparse-data-driven-constitutive-modeling-via-transfer-learning-in-physics-encoded-neural-networks/455649/",{"url":99,"name":65,"@type":101,"image":102,"author":107,"headline":65,"publisher":109,"fileFormat":112,"inLanguage":74,"description":66,"dateModified":113,"datePublished":114,"encodingFormat":112,"isAccessibleForFree":115,"interactionStatistic":116},"DigitalDocument",{"url":103,"@type":104,"width":105,"height":106},"https://docshare.wps.com/thumbnails/practical-sparse-data-driven-constitutive-modeling-via-transfer-learning-in-physics-encoded-neural-networks/455649.png","ImageObject",300,407,{"name":63,"@type":108},"Person",{"url":91,"name":110,"@type":111},"DocShare","Organization","application/pdf","2026-10-05","2026-09-30",true,{"@type":117,"interactionType":118,"userInteractionCount":72},"InteractionCounter",{"@type":119},"ViewAction",{"@type":121,"mainEntity":122},"FAQPage",[123,129,133],{"name":124,"@type":125,"acceptedAnswer":126},"What problem does the study address in physics-encoded neural networks calibration?","Question",{"text":127,"@type":128},"It addresses calibration difficulty when only limited experimental data are available, which makes reliable physics-embedded training challenging.","Answer",{"name":130,"@type":125,"acceptedAnswer":131},"How does the study use transfer learning in this framework?",{"text":132,"@type":128},"It pre-trains PeNNs on synthetic labeled data generated from traditional constitutive models, then fine-tunes them using implicitly labeled data derived from high-fidelity experimental records.",{"name":134,"@type":125,"acceptedAnswer":135},"How are the resulting models evaluated?",{"text":136,"@type":128},"The fine-tuned PeNNs are integrated into FEM software as user material models and assessed through extensive drained and undrained triaxial test simulations, analyzing effects of data volume and fine-tuning configurations.","https://schema.org",{"og:url":99,"og:type":139,"og:title":65,"og:site_name":110,"og:description":66},"article",{"robots":141,"canonical":99},"index,follow",{"doc_id":61,"site_id":75},1791061359]