[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125900-en":3,"doc-seo-125900-105":31,"detail-sidebar-cat-0-en-105":96},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125900,2336474466712,"Maeve","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine learning for robust structural uncertainty quantification in fractured reservoirs - Article","Including uncertainty is essential for accurate decision-making in underground applications. A novel machine-learning approach is proposed to account for structural uncertainty in two enhanced geothermal systems (EGS) by leveraging ML models to emulate numerical simulation outputs. Small changes in structural models can strongly alter tracer breakthrough curves (BTCs). Three ML regressors are trained and compared: decision tree regression, random forest regression, and a chain-based gradient boosting regression that predicts each BTC time step while capturing correlations across consecutive steps. Replacing the numerical solver reduces computation time by six orders of magnitude, enabling BTCs for 2′000 reservoir models and comprehensive structural uncertainty quantification.","Geothermics 120 (2024) 103012  \nContents lists available at ScienceDirect  \nGeothermics  \njournal [homepage:](homepage: www.elsevier.com/locate/geothermics)[ www.elsevier.com/locate/geothermics](homepage: www.elsevier.com/locate/geothermics)  \n| Machine learning for robust structural uncertainty quantification in fractured reservoirs\u003Cbr>Ali Dashtia, *, Thilo Stadelmann b, Thomas Kohl a\u003Cbr>a Institute of Applied Geosciences, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany\u003Cbr>b Centre for AI, Technikumstrasse 71, Zurich University of Applied Sciences, 8400 Winterthur, Switzerland |  |  |\n| --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |\n| Keywords:\u003Cbr>Machine learning Uncertainty quantification Structural uncertainty EGS |  | Including uncertainty is essential for accurate decision-making in underground applications. We propose a novel approach to consider structural uncertainty in two enhanced geothermal systems (EGSs) using machine learning (ML) models. The results of numerical simulations show that a small change in the structural model can cause a significant variation in the tracer breakthrough curves (BTCs). To develop a more robust method for including structural uncertainty, we train three different ML models: decision tree regression (DTR), random forest regression (RFR), and gradient boosting regression (GBR). DTR and RFR predict the entire BTC at once, but they are susceptible to overfitting and underfitting. In contrast, GBR predicts each time step of the BTC as a separate target variable, considering the possible correlation between consecutive time steps. This approach is implemented using a chain of regression models. The chain model achieves an acceptable increase in RMSE from train to test data, confirming its ability to capture both the general trend and small-scale heterogeneities of the BTCs. Additionally, using the ML model instead of the numerical solver reduces the computational time by six orders of magnitude. This time efficiency allows us to calculate BTCs for 2′000 different reservoir models, enabling a more comprehensive structural uncertainty quantification for EGS cases. The chain model is particularly promising, as it is robust to overfitting and underfitting and can generate BTCs for a large number of structural models efficiently. |\n\n1. Introduction  \nNumerical simulations of physical systems described by differential equations are essential in engineering. Advancements in hardware have enabled computing units to solve coupled nonlinear differential equations, encompassing a wide range of phenomena, from weather forecasting (Bauer et al., 2015) to blood circulation in living bodies (Doost et al., 2016). However, these methods are computationally intensive and highly sensitive to specific cases. Besides the huge energy consumption of these computational infrastructures (Benoit et al., 2018), their availability is also limited. Furthermore, parameter tuning, sensitivity analysis (Borgonovo and Plischke, 2016), and uncertainty quantification (Abbaszadeh Shahri et al., 2022; Soize, 2017) demand up to millions of simulations.  \nMachine learning (ML) methods have gained significant traction across various fields (Brunton and Kutz, 2022; Stadelmann et al., 2019), including geothermal applications (Okoroafor et al., 2022). In this context, data-driven and physics-informed ML (physics-informed neural  \nnetwork, PINN) techniques are of great interest (Carleo et al., 2019; Raissi et al., 2019). PINNs and their diverse descendants are ceaselessly flourishing to replace numerical solvers (Karniadakis et al., 2021; Kharazmi et al., 2019; Knapp et al., 2021; Yu et al., 2022); however, their accuracy and time-efficiency for solving complex problems is still a subject of development (Degen et al., 2023).  \nOne of the challenges in geothermal applications is characterizing fluid flow through complex underground networks. While the geometry of a fracture can define the general direction","cbCaiksBEUegPs89","https://ap.wps.com/l/cbCaiksBEUegPs89","pdf",6467993,4,1,11,"English","en",105,"# Introduction\n## Geothermal simulations and uncertainty challenges\n## Machine learning for physics and surrogate modeling\n## Tracer tests, breakthrough curves, and structural uncertainty","[{\"question\":\"Why is structural uncertainty important for enhanced geothermal systems (EGS)?\",\"answer\":\"Structural uncertainty affects tracer breakthrough curves (BTCs), and small changes in the structural model can produce large variations. Accounting for this uncertainty is crucial for reliable underground decision-making.\"},{\"question\":\"Which machine learning models are used to quantify structural uncertainty?\",\"answer\":\"The study trains three models: decision tree regression (DTR), random forest regression (RFR), and a chain-based gradient boosting regression (GBR).\"},{\"question\":\"How does the chain-based GBR improve BTC prediction compared with DTR and RFR?\",\"answer\":\"DTR and RFR predict the entire BTC at once but may suffer from overfitting or underfitting. The chain model predicts each BTC time step separately as targets and models correlations between consecutive time steps using a regression chain.\"},{\"question\":\"What computational benefit does the ML approach provide?\",\"answer\":\"Using the ML surrogate instead of the numerical solver reduces computation time by about six orders of magnitude, allowing BTC calculations for 2′000 reservoir models and broader uncertainty quantification.\"}]","Machine learning for robust structural uncertainty quantification in fractured reservoirs - Article | PDF",1785901922,28,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":91,"head_meta":93,"extra_data":95,"updated_unix":29},"machine-learning-for-robust-structural-uncertainty-quantification-in-fractured-reservoirs-article","",{"@graph":37,"@context":90},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":20},"https://docshare.wps.com/document/machine-learning-for-robust-structural-uncertainty-quantification-in-fractured-reservoirs-article/125900/",{"url":53,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-22","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82,86],{"name":73,"@type":74,"acceptedAnswer":75},"Why is structural uncertainty important for enhanced geothermal systems (EGS)?","Question",{"text":76,"@type":77},"Structural uncertainty affects tracer breakthrough curves (BTCs), and small changes in the structural model can produce large variations. Accounting for this uncertainty is crucial for reliable underground decision-making.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which machine learning models are used to quantify structural uncertainty?",{"text":81,"@type":77},"The study trains three models: decision tree regression (DTR), random forest regression (RFR), and a chain-based gradient boosting regression (GBR).",{"name":83,"@type":74,"acceptedAnswer":84},"How does the chain-based GBR improve BTC prediction compared with DTR and RFR?",{"text":85,"@type":77},"DTR and RFR predict the entire BTC at once but may suffer from overfitting or underfitting. The chain model predicts each BTC time step separately as targets and models correlations between consecutive time steps using a regression chain.",{"name":87,"@type":74,"acceptedAnswer":88},"What computational benefit does the ML approach provide?",{"text":89,"@type":77},"Using the ML surrogate instead of the numerical solver reduces computation time by about six orders of magnitude, allowing BTC calculations for 2′000 reservoir models and broader uncertainty quantification.","https://schema.org",{"og:url":53,"og:type":92,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":94,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":97},[98,102,106,110,115,120,125,128,133,136,140],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":107,"show_sort_weight":108,"slug":109},"Exam",70,"exam",{"id":111,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":113,"slug":114},5,"Comic",60,"comic",{"id":116,"doc_module":4,"doc_module_name":47,"category_name":117,"show_sort_weight":118,"slug":119},6,"Technology",50,"technology",{"id":121,"doc_module":4,"doc_module_name":47,"category_name":122,"show_sort_weight":123,"slug":124},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":126,"slug":127},30,"research-report",{"id":129,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":131,"slug":132},9,"Religion & Spirituality",20,"religion-spirituality",{"id":131,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":131,"slug":135},"World Cup","world-cup",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":137,"slug":139},10,"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":47,"category_name":142,"show_sort_weight":111,"slug":143},19,"General","general"]