利用傅里叶神经算子加速多孔介质流动模拟:在二氧化碳地质封存中的应用

IF 2.9 4区 工程技术 Q1 MULTIDISCIPLINARY SCIENCES
Anirban Chandra, Marius Koch, Suraj Pawar, Aniruddha Panda, Kamyar Azizzadenesheli, Jeroen Snippe, Faruk O. Alpak, Farah Hariri, Clement Etienam, Pandu Devarakota, Anima Anandkumar, Detlef Hohl
{"title":"利用傅里叶神经算子加速多孔介质流动模拟:在二氧化碳地质封存中的应用","authors":"Anirban Chandra, Marius Koch, Suraj Pawar, Aniruddha Panda, Kamyar Azizzadenesheli, Jeroen Snippe, Faruk O. Alpak, Farah Hariri, Clement Etienam, Pandu Devarakota, Anima Anandkumar, Detlef Hohl","doi":"10.1002/adts.202500747","DOIUrl":null,"url":null,"abstract":"This study aims to develop surrogate models to accelerate decision-making processes related to porous media flows, using geologic storage of carbon dioxide (<span data-altimg=\"/cms/asset/fe9d33ec-8e95-4fb7-aed8-413e06185e8c/adts70131-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"4\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/adts70131-math-0001.png\"><mjx-semantics><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0001\" display=\"inline\" location=\"graphic/adts70131-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">C</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msub data-semantic-=\"\" data-semantic-children=\"1,2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">O</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container>) as an example. Several engineering problems, including selection of subsurface <span data-altimg=\"/cms/asset/c6fdbd4b-0066-4ff3-861c-d71252002e49/adts70131-math-0002.png\"></span><mjx-container ctxtmenu_counter=\"5\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/adts70131-math-0002.png\"><mjx-semantics><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0002\" display=\"inline\" location=\"graphic/adts70131-math-0002.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">C</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msub data-semantic-=\"\" data-semantic-children=\"1,2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">O</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container> storage sites, often requires costly and complex simulations of flow fields. In this work, a Fourier Neural Operator (FNO) based model is developed for real-time, high-resolution simulation of <span data-altimg=\"/cms/asset/48e59dd4-68c1-4e31-b85d-28a1a3d27bcd/adts70131-math-0003.png\"></span><mjx-container ctxtmenu_counter=\"6\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/adts70131-math-0003.png\"><mjx-semantics><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic- data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0003\" display=\"inline\" location=\"graphic/adts70131-math-0003.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,3\" data-semantic-content=\"4\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper C upper O 2\" data-semantic-type=\"infixop\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">C</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msub data-semantic-=\"\" data-semantic-children=\"1,2\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\">O</mi><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container> plume migration. The model is trained on a comprehensive dataset derived from realistic subsurface parameters and achieves a computational speed-up of <span data-altimg=\"/cms/asset/8318ab87-c4db-40cd-b9c8-1ef73b221531/adts70131-math-0004.png\"></span><mjx-container ctxtmenu_counter=\"7\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/adts70131-math-0004.png\"><mjx-semantics><mjx-mrow data-semantic-children=\"0,13\" data-semantic-content=\"14,0\" data-semantic- data-semantic-role=\"simple function\" data-semantic-speech=\"script upper O left parenthesis 10 cubed t o 10 Superscript 5 Baseline right parenthesis\" data-semantic-type=\"appl\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"15\" data-semantic-role=\"simple function\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"15\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"12\" data-semantic-content=\"1,9\" data-semantic- data-semantic-parent=\"15\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,5,8\" data-semantic-content=\"10,11\" data-semantic- data-semantic-parent=\"13\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msup data-semantic-children=\"2,3\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-script style=\"vertical-align: 0.393em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\"6,7\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-script style=\"vertical-align: 0.393em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"margin-left: 0.056em; margin-right: 0.056em;\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0004\" display=\"inline\" location=\"graphic/adts70131-math-0004.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"0,13\" data-semantic-content=\"14,0\" data-semantic-role=\"simple function\" data-semantic-speech=\"script upper O left parenthesis 10 cubed t o 10 Superscript 5 Baseline right parenthesis\" data-semantic-type=\"appl\"><mi data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic-operator=\"appl\" data-semantic-parent=\"15\" data-semantic-role=\"simple function\" data-semantic-type=\"identifier\" mathvariant=\"script\">O</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"appl\" data-semantic-parent=\"15\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\">⁡</mo><mrow data-semantic-=\"\" data-semantic-children=\"12\" data-semantic-content=\"1,9\" data-semantic-parent=\"15\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mo data-semantic-=\"\" data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"open\" data-semantic-type=\"fence\" stretchy=\"false\">(</mo><mrow data-semantic-=\"\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,5,8\" data-semantic-content=\"10,11\" data-semantic-parent=\"13\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><msup data-semantic-=\"\" data-semantic-children=\"2,3\" data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\">10</mn><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\">3</mn></msup><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><mi data-semantic-=\"\" data-semantic-font=\"normal\" data-semantic-parent=\"12\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\">to</mi><mo data-semantic-=\"\" data-semantic-added=\"true\" data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\">⁢</mo><msup data-semantic-=\"\" data-semantic-children=\"6,7\" data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\">10</mn><mn data-semantic-=\"\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic-parent=\"8\" data-semantic-role=\"integer\" data-semantic-type=\"number\">5</mn></msup></mrow><mo data-semantic-=\"\" data-semantic-operator=\"fenced\" data-semantic-parent=\"13\" data-semantic-role=\"close\" data-semantic-type=\"fence\" stretchy=\"false\">)</mo></mrow></mrow>$\\mathcal {O}(10^3 \\textrm { to } 10^5)$</annotation></semantics></math></mjx-assistive-mml></mjx-container> when compared to numerical simulators used in this work, with only a minimal reduction in predictive accuracy. Super-resolution experiments are also investigated to reduce the computational cost of training the FNO-based models. Additionally, various strategies are proposed to enhance the reliability of model predictions, which is crucial for evaluating actual geological storage sites. This framework, based on NVIDIA's PhysicsNeMo library, enables rapid screening of sites for CCS. This work scales data-driven models to realistic 3D systems that better reflect real-life subsurface aquifers and reservoirs, paving the way for building next-generation digital twins for subsurface CCS applications. The workflows and strategies discussed can be easily adapted to other material systems and energy solutions, such as geothermal reservoir modeling, flow batteries, fuel cells, and hydrogen storage.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"16 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Accelerating Porous Media Flow Simulations With Fourier Neural Operators: An Application to Geologic Storage of CO2\",\"authors\":\"Anirban Chandra, Marius Koch, Suraj Pawar, Aniruddha Panda, Kamyar Azizzadenesheli, Jeroen Snippe, Faruk O. Alpak, Farah Hariri, Clement Etienam, Pandu Devarakota, Anima Anandkumar, Detlef Hohl\",\"doi\":\"10.1002/adts.202500747\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This study aims to develop surrogate models to accelerate decision-making processes related to porous media flows, using geologic storage of carbon dioxide (<span data-altimg=\\\"/cms/asset/fe9d33ec-8e95-4fb7-aed8-413e06185e8c/adts70131-math-0001.png\\\"></span><mjx-container ctxtmenu_counter=\\\"4\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/adts70131-math-0001.png\\\"><mjx-semantics><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"1,2\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0001\\\" display=\\\"inline\\\" location=\\\"graphic/adts70131-math-0001.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">C</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"1,2\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">O</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container>) as an example. Several engineering problems, including selection of subsurface <span data-altimg=\\\"/cms/asset/c6fdbd4b-0066-4ff3-861c-d71252002e49/adts70131-math-0002.png\\\"></span><mjx-container ctxtmenu_counter=\\\"5\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/adts70131-math-0002.png\\\"><mjx-semantics><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"1,2\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0002\\\" display=\\\"inline\\\" location=\\\"graphic/adts70131-math-0002.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">C</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"1,2\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">O</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container> storage sites, often requires costly and complex simulations of flow fields. In this work, a Fourier Neural Operator (FNO) based model is developed for real-time, high-resolution simulation of <span data-altimg=\\\"/cms/asset/48e59dd4-68c1-4e31-b85d-28a1a3d27bcd/adts70131-math-0003.png\\\"></span><mjx-container ctxtmenu_counter=\\\"6\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/adts70131-math-0003.png\\\"><mjx-semantics><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"1,2\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0003\\\" display=\\\"inline\\\" location=\\\"graphic/adts70131-math-0003.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"0,3\\\" data-semantic-content=\\\"4\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C upper O 2\\\" data-semantic-type=\\\"infixop\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">C</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msub data-semantic-=\\\"\\\" data-semantic-children=\\\"1,2\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\">O</mi><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">2</mn></msub></mrow>$CO_2$</annotation></semantics></math></mjx-assistive-mml></mjx-container> plume migration. The model is trained on a comprehensive dataset derived from realistic subsurface parameters and achieves a computational speed-up of <span data-altimg=\\\"/cms/asset/8318ab87-c4db-40cd-b9c8-1ef73b221531/adts70131-math-0004.png\\\"></span><mjx-container ctxtmenu_counter=\\\"7\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" role=\\\"application\\\" sre-explorer- style=\\\"font-size: 103%; position: relative;\\\" tabindex=\\\"0\\\"><mjx-math aria-hidden=\\\"true\\\" location=\\\"graphic/adts70131-math-0004.png\\\"><mjx-semantics><mjx-mrow data-semantic-children=\\\"0,13\\\" data-semantic-content=\\\"14,0\\\" data-semantic- data-semantic-role=\\\"simple function\\\" data-semantic-speech=\\\"script upper O left parenthesis 10 cubed t o 10 Superscript 5 Baseline right parenthesis\\\" data-semantic-type=\\\"appl\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"script\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"application\\\" data-semantic-type=\\\"punctuation\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"12\\\" data-semantic-content=\\\"1,9\\\" data-semantic- data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"4,5,8\\\" data-semantic-content=\\\"10,11\\\" data-semantic- data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mjx-msup data-semantic-children=\\\"2,3\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-script style=\\\"vertical-align: 0.393em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo><mjx-msup data-semantic-children=\\\"6,7\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mn><mjx-script style=\\\"vertical-align: 0.393em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"margin-left: 0.056em; margin-right: 0.056em;\\\"><mjx-c></mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml display=\\\"inline\\\" unselectable=\\\"on\\\"><math altimg=\\\"urn:x-wiley:25130390:media:adts70131:adts70131-math-0004\\\" display=\\\"inline\\\" location=\\\"graphic/adts70131-math-0004.png\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><semantics><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"0,13\\\" data-semantic-content=\\\"14,0\\\" data-semantic-role=\\\"simple function\\\" data-semantic-speech=\\\"script upper O left parenthesis 10 cubed t o 10 Superscript 5 Baseline right parenthesis\\\" data-semantic-type=\\\"appl\\\"><mi data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"script\\\" data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"identifier\\\" mathvariant=\\\"script\\\">O</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"application\\\" data-semantic-type=\\\"punctuation\\\">⁡</mo><mrow data-semantic-=\\\"\\\" data-semantic-children=\\\"12\\\" data-semantic-content=\\\"1,9\\\" data-semantic-parent=\\\"15\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" stretchy=\\\"false\\\">(</mo><mrow data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"4,5,8\\\" data-semantic-content=\\\"10,11\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"2,3\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">10</mn><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">3</mn></msup><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><mi data-semantic-=\\\"\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"identifier\\\">to</mi><mo data-semantic-=\\\"\\\" data-semantic-added=\\\"true\\\" data-semantic-operator=\\\"infixop,⁢\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\">⁢</mo><msup data-semantic-=\\\"\\\" data-semantic-children=\\\"6,7\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">10</mn><mn data-semantic-=\\\"\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\">5</mn></msup></mrow><mo data-semantic-=\\\"\\\" data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" stretchy=\\\"false\\\">)</mo></mrow></mrow>$\\\\mathcal {O}(10^3 \\\\textrm { to } 10^5)$</annotation></semantics></math></mjx-assistive-mml></mjx-container> when compared to numerical simulators used in this work, with only a minimal reduction in predictive accuracy. Super-resolution experiments are also investigated to reduce the computational cost of training the FNO-based models. Additionally, various strategies are proposed to enhance the reliability of model predictions, which is crucial for evaluating actual geological storage sites. This framework, based on NVIDIA's PhysicsNeMo library, enables rapid screening of sites for CCS. This work scales data-driven models to realistic 3D systems that better reflect real-life subsurface aquifers and reservoirs, paving the way for building next-generation digital twins for subsurface CCS applications. The workflows and strategies discussed can be easily adapted to other material systems and energy solutions, such as geothermal reservoir modeling, flow batteries, fuel cells, and hydrogen storage.\",\"PeriodicalId\":7219,\"journal\":{\"name\":\"Advanced Theory and Simulations\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advanced Theory and Simulations\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/adts.202500747\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Theory and Simulations","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/adts.202500747","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

摘要

本研究旨在建立替代模型,以二氧化碳(C±O2$CO_2$)的地质储存为例,加速与多孔介质流动相关的决策过程。一些工程问题,包括地下C²O2$CO_2$储存地点的选择,往往需要昂贵和复杂的流场模拟。本文建立了一种基于傅立叶神经算子(Fourier Neural Operator, FNO)的实时、高分辨率模拟C²O2$CO_2$羽流迁移的模型。该模型是在基于真实地下参数的综合数据集上进行训练的,与本研究中使用的数值模拟器相比,该模型的计算速度提高了O (103 ~ 105)$\mathcal {O}(10^3 \textrm{到}10^5)$,预测精度只有很小的降低。为了减少基于fno的模型训练的计算成本,还研究了超分辨率实验。此外,提出了各种策略来提高模型预测的可靠性,这对于评估实际的地质储存地点至关重要。该框架基于NVIDIA的physicsnmo库,可以快速筛选CCS的站点。这项工作将数据驱动模型扩展到真实的3D系统,更好地反映真实的地下含水层和水库,为构建下一代地下CCS应用的数字孪生体铺平了道路。所讨论的工作流程和策略可以很容易地适用于其他材料系统和能源解决方案,如地热储层建模、液流电池、燃料电池和氢储存。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Accelerating Porous Media Flow Simulations With Fourier Neural Operators: An Application to Geologic Storage of CO2

Accelerating Porous Media Flow Simulations With Fourier Neural Operators: An Application to Geologic Storage of CO2
This study aims to develop surrogate models to accelerate decision-making processes related to porous media flows, using geologic storage of carbon dioxide (CO2$CO_2$) as an example. Several engineering problems, including selection of subsurface CO2$CO_2$ storage sites, often requires costly and complex simulations of flow fields. In this work, a Fourier Neural Operator (FNO) based model is developed for real-time, high-resolution simulation of CO2$CO_2$ plume migration. The model is trained on a comprehensive dataset derived from realistic subsurface parameters and achieves a computational speed-up of O(103to105)$\mathcal {O}(10^3 \textrm { to } 10^5)$ when compared to numerical simulators used in this work, with only a minimal reduction in predictive accuracy. Super-resolution experiments are also investigated to reduce the computational cost of training the FNO-based models. Additionally, various strategies are proposed to enhance the reliability of model predictions, which is crucial for evaluating actual geological storage sites. This framework, based on NVIDIA's PhysicsNeMo library, enables rapid screening of sites for CCS. This work scales data-driven models to realistic 3D systems that better reflect real-life subsurface aquifers and reservoirs, paving the way for building next-generation digital twins for subsurface CCS applications. The workflows and strategies discussed can be easily adapted to other material systems and energy solutions, such as geothermal reservoir modeling, flow batteries, fuel cells, and hydrogen storage.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Advanced Theory and Simulations
Advanced Theory and Simulations Multidisciplinary-Multidisciplinary
CiteScore
5.50
自引率
3.00%
发文量
221
期刊介绍: Advanced Theory and Simulations is an interdisciplinary, international, English-language journal that publishes high-quality scientific results focusing on the development and application of theoretical methods, modeling and simulation approaches in all natural science and medicine areas, including: materials, chemistry, condensed matter physics engineering, energy life science, biology, medicine atmospheric/environmental science, climate science planetary science, astronomy, cosmology method development, numerical methods, statistics
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信