[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119536-en":3,"doc-seo-119536-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119536,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Enhancing inverse modeling in groundwater systems through machine learning - a comprehensive comparative study","Tandem neural network architecture (TNNA) is assessed for estimating uncertain parameters via inverse mappings, with reliability examined beyond limited prior scenarios. A systematic comparison is conducted against four traditional metaheuristic algorithms across three heterogeneity inversion frameworks, combining surrogate models with either optimization alone, Karhunen–Loève expansion (KLE) dimensionality reduction, or generative machine-learning dimensionality reduction for Gaussian and non-Gaussian random fields. Performance under multiplicative Gaussian noise levels of 1% and 10% is analyzed for normalized hydraulic head and solute concentration, showing convergence-accurate and robust inversions with stronger constraints at higher noise. TNNA delivers more reliable results and significantly improved computational efficiency in groundwater system inversions.","Hydrol. Earth Syst. Sci., 29, 4251–4279, 2025 [https://doi.org/10.5194/hess-29-4251-2025](https://doi.org/10.5194/hess-29-4251-2025)[ ](https://doi.org/10.5194/hess-29-4251-2025)© Author(s) 2025 . This work is distributed under the Creative Commons Attribution 4 .0 License.  \nEnhancing inverse modeling in groundwater systems through machine learning: a comprehensive comparative study  \nJunjun Chen 1,2 , Zhenxue Dai2,3 , Shangxian Yin4 , Mingkun Zhang5 , and Mohamad Reza Soltanian6  \n1National and Local Joint Engineering Laboratory of Internet Application Technology on Mine, China University of Mining and Technology, Xuzhou, 221008, China  \n2 College of Construction Engineering, Jilin University, Changchun, 130026, China  \n3 School of Environmental and Municipal Engineering, Qingdao University of Technology, Qingdao, 273400, China  \n4 College of Safety Engineering, North China Institute of Science and Technology, Langfang, 065201, China  \n5 Shandong Ruyi Technology Group Co., Ltd., Jinan, 250000, China  \n6Departments of Geosciences and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45220, USA Correspondence: Zhenxue Dai ([dzx@jlu.edu.cn](dzx@jlu.edu.cn)) and Shangxian Yin ([yinshx03@126.com](yinshx03@126.com))  \nReceived: 12 October 2024 – Discussion started: 6 December 2024  \nRevised: 9 June 2025 – Accepted: 16 June 2025 – Published: 10 September 2025  \nAbstract. Tandem neural network architecture (TNNA) is a machine learning algorithm that has recently been proposed for estimating uncertain parameters with inverse mappings. However, its reliability has only been validated in limited research scenarios, and its advantages over conventional methods remain underexplored. This study systematically compares the performance of the TNNA algorithm to four traditional metaheuristic algorithms across three heterogeneity scenarios, each employing a specific inversion framework:(i) a surrogate model coupled with an optimization algorithm for cases with eight homogeneous parameter zones,(ii) Karhunen–Loève expansion (KLE)-based dimensionality reduction combined with a surrogate model and an optimization algorithm for a high-dimensional Gaussian random field, and (iii) generative machine-learning-based dimensionality reduction integrated with a surrogate model and an optimization algorithm for a high-dimensional non-Gaussian random field. Additionally, we evaluate algorithm performance under two different noise-level conditions (multiplicative Gaussian noise with standard deviations of 1 % and 10 %) for normalized hydraulic head and solute concentration data in the non-Gaussian random field scenario, which exhibits the most complex parameter characteristics. The results demonstrate that both the TNNA algorithm and the metaheuristic algorithms achieve inversion results that satisfy the convergence accuracy within these machine-learning-based inversion frameworks. Moreover, under the 10 % high-noise con-  \ndition in the non-Gaussian random field, the inversion results remain robust when sufficient constraints are imposed. Compared to metaheuristic approaches, the TNNA method yields more reliable inversion results with significantly higher computational efficiency, highlighting the considerable advantages of machine learning in advancing groundwater system inversions.  \n1 Introduction  \nNumerical models are essential for quantifying flow and mass transport dynamics within aquifers, providing significant insights into hydrological and biogeochemical processes (Steefel et al., 2005; Sanchez-Vila et al., 2010; Sternagelet al., 2021; Xu et al., 2022) . However, directly measuring aquifer parameters, such as permeability fields, remains challenging due to limitations in the current hydrogeological exploration techniques and budgetary constraints (Yeh, 1986; Kool et al., 1987; Beven and Binley, 1992; McLaughlin and Townley, 1996; Dai and Samper, 2004; Castaings et al., 2009; Chen et al., 2021) . Inverse modeling has become a key approach ","cbCaigpbwz4fLiHE","https://ap.wps.com/l/cbCaigpbwz4fLiHE","pdf",16794050,1,29,"English","en",105,"# Introduction\n## Numerical models and inverse modeling in aquifers\n## Bayesian data assimilation and optimization-based inversion\n## Local optimization methods and risks of local optima\n## Metaheuristic global search methods","[{\"question\":\"What problem does the TNNA method address in groundwater inverse modeling?\",\"answer\":\"TNNA estimates uncertain parameters by learning inverse mappings, aiming to improve the reliability of parameter estimation used in groundwater numerical simulations.\"},{\"question\":\"How is the study designed to compare TNNA with traditional metaheuristics?\",\"answer\":\"TNNA is compared with four metaheuristic algorithms under three heterogeneity scenarios, each embedded in a specific inversion framework that uses surrogate models with different dimensionality-reduction strategies.\"},{\"question\":\"What noise conditions are evaluated and what impact do they have?\",\"answer\":\"The study evaluates multiplicative Gaussian noise with standard deviations of 1% and 10%. Under the higher 10% noise in the non-Gaussian random-field case, inversion results remain robust when sufficient constraints are imposed.\"}]","Enhancing inverse modeling in groundwater systems through machine learning - a comprehensive comparative study | PDF",1785724832,73,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"enhancing-inverse-modeling-in-groundwater-systems-through-machine-learning-a-comprehensive-comparative-study","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/enhancing-inverse-modeling-in-groundwater-systems-through-machine-learning-a-comprehensive-comparative-study/119536/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the TNNA method address in groundwater inverse modeling?","Question",{"text":75,"@type":76},"TNNA estimates uncertain parameters by learning inverse mappings, aiming to improve the reliability of parameter estimation used in groundwater numerical simulations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the study designed to compare TNNA with traditional metaheuristics?",{"text":80,"@type":76},"TNNA is compared with four metaheuristic algorithms under three heterogeneity scenarios, each embedded in a specific inversion framework that uses surrogate models with different dimensionality-reduction strategies.",{"name":82,"@type":73,"acceptedAnswer":83},"What noise conditions are evaluated and what impact do they have?",{"text":84,"@type":76},"The study evaluates multiplicative Gaussian noise with standard deviations of 1% and 10%. Under the higher 10% noise in the non-Gaussian random-field case, inversion results remain robust when sufficient constraints are imposed.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]