[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120004-en":3,"doc-seo-120004-105":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},120004,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Hybrid Machine Learning Algorithms for Solving Forward and Inverse Problems in Physical Sciences - Dissertation","Machine learning techniques enable faster forward simulations and parameter discovery from limited data for differential equations, especially partial differential equations (PDEs). Numerical accuracy remains difficult when real-time inference is required and when problems must be solved in inverse settings. This dissertation develops hybrid strategies that combine classical finite discretization methods with modern ML to improve accuracy while preserving computational efficiency. The work targets challenges at the intersection of scientific computing, machine learning, and applied mathematics.","UC Santa Barbara  \nUC Santa Barbara Electronic Theses and Dissertations  \nTitle  \nHybrid Machine Learning Algorithms for Solving Forward and Inverse Problems in Physical Sciences  \nPermalink  \n[https://escholarship.org/uc/item/8cm0s7kz](https://escholarship.org/uc/item/8cm0s7kz)  \nAuthor  \nPakravan, Samira  \nPublication Date  \n2024  \nPeer reviewed|Thesis/dissertation  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nUniversity of California  \nSanta Barbara  \nHybrid Machine Learning Algorithms for Solving Forward and Inverse Problems in Physical Sciences  \nA dissertation submitted in partial satisfaction  \nof the requirements for the degree  \nDoctor of Philosophy  \nin  \nMechanical Engineering  \nby  \nSamira Pakravan  \nCommittee in charge:  \nProfessor Frederic G. Gibou, Chair  \nProfessor Tresa M. Pollock  \nProfessor Enoch Yeung  \nProfessor Paolo Luzzatto-Fegiz  \nThe Dissertation of Samira Pakravan is approved.  \n\n| Professor Tresa M. Pollock |\n| --- |\n| Professor Enoch Yeung |\n| Professor Paolo Luzzatto-Fegiz |\n\nProfessor Frederic G. Gibou, Committee Chair  \nJune 2024  \nHybrid Machine Learning Algorithms for Solving Forward and Inverse Problems in  \nPhysical Sciences  \nCopyright © 2024  \nby  \nSamira Pakravan  \nTo My Parents & Pouria  \nAcknowledgements  \nI am immensely grateful to the individuals who have supported me throughout my doctoral journey. First and foremost, my sincere gratitude go to Professor Frederic G. Gibou, my advisor, for his guidance, encouragement, and patience. His belief in my abilities has been a constant source of motivation.  \nI am also grateful to my dissertation committee members, Professor Tresa M. Pollock, Professor Paolo Luzzatto-Fegiz, and Professor Enoch Yeung, for their valuable input and support. Their expertise has been invaluable in shaping my work.  \nTo my loving husband, Pouria, words cannot express the depth of my gratitude foryour support and boundless patience. Your counsel and love have illuminated my path, offering perspective and solace both in my research and in life. I am endlessly grateful for your companionship and the countless sacrifices you’ve made to see me succeed.  \nI am deeply appreciative of the sacrifices made by my parents, Zahra and Mohammadtaghi, both of whom dedicated their lives to education. Their commitment to fostering learning has deeply inspired my own passion for teaching. As a teaching assistant, I have been driven by their example to work diligently and passionately. Additionally, Iam thankful for the steadfast support of my sister, Parisa, especially during the past decade when her presence was sorely missed, and my brother, Alireza, for his unwavering presence and encouragement.  \nI would like to express my heartfelt thanks to my dear friends Anees and Mitra for their incredible kindness, their belief in me and words of encouragement that carried me through the toughest of times. Ghazaleh and Behzad, I am grateful for the late-night conversations, and the shared moments of celebration that have enriched this journey.  \nTo each and every person who has touched my life and contributed to my journey, Iam forever grateful for your presence in my life.  \nCurriculum Vitæ  \nSamira Pakravan  \nEducation  \n2024 Ph.D. in Mechanical Engineering (Expected), University of Califor  \nnia, Santa Barbara, USA.  \n2015 M.S. in Computer Science, New Mexico State University, USA.  \n2012 [B.S. in](B.S. in) Computer Science, Sadjad Institute of Higher Education,  \nIran.  \nPublications  \n(†: equal contribution)  \n• Journal papers:  \n1. P Mistani†, S Pakravan†, R Ilango, F Gibou. JAX-DIPS: neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities, Journal of Computational Physics, 2023 [1]  \n2. S Pakravan†, P Mistani†, MA Aragon-Calvo, F Gibou. Solving inverse-PDE problems with physics-aware neural networks, Journal of Computational Physics, 2021 [2]  \n3. P Mistani, S Pakra","cbCailBhynfYra77","https://ap.wps.com/l/cbCailBhynfYra77","pdf",19043584,1,143,"English","en",105,"# Dissertation Context\n## Title and Authorship\n## Publication Information\n# Contributions and Motivation\n## Hybrid Strategies for Forward and Inverse Solving\n## Accuracy vs. Computational Efficiency\n# Academic Background\n## Education\n## Publications\n### Journal Papers\n### Conference Workshops on AI\n### Book Chapters\n# Acknowledgements","[{\"question\":\"Why combine classical finite discretization methods with machine learning in this dissertation?\",\"answer\":\"To improve numerical accuracy for forward simulations and inverse problem-solving while maintaining computational efficiency.\"},{\"question\":\"What problem settings does the dissertation focus on?\",\"answer\":\"Differential equations, particularly PDEs, especially cases requiring real-time inference and inverse problem solutions from limited data.\"},{\"question\":\"What are the dissertation’s main goals at the intersection of fields?\",\"answer\":\"Address key challenges across scientific computing, machine learning, and applied mathematics by developing hybrid approaches for solving forward and inverse problems.\"}]","Hybrid Machine Learning Algorithms for Solving Forward and Inverse Problems in Physical Sciences - 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