Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Survey of Probabilistic and Non-Probabilistic Approaches in Forward and Inverse Problems

[2408.08629] Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Survey of Probabilistic and Non-Probabilistic Approaches in Forward and Inverse Problems Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2408.08629 (cs) [Submitted on 16 Aug 2024 ( v1 ), last revised 19 Oct 2025 (this version, v2)] Title: Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Survey of Probabilistic and Non-Probabilistic Approaches in Forward and Inverse Problems Authors: Wang-Ji Yan (1 and 2), Lin-Feng Mei (1), Jiang Mo (1), Costas Papadimitriou (3), Ka-Veng Yuen (1 and 2), Michael Beer (4,5, and 6) ((1) State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, (2) Guangdong-Hong Kong-Macau Joint Laboratory for Smart Cities, China, (3) Department of Mechanical Engineering, University of Thessaly, (4) Leibniz University Hannover, Institute for Risk and Reliability, (5) Department of Civil and Environmental Engineering, University of Liverpool, (6) International Joint Research Center for Resilient Infrastructure & International Joint Research Center for Engineering Reliability and Stochastic Mechanics, Tongji University) View PDF Abstract: In the era of big data, machine learning (ML) has become a powerful tool in various fields, notably impacting structural dynamics. ML algorithms offer advantages by modeling physical phenomena based on data, even in the absence of underlying mechanisms. However, uncertainties such as measurement noise and modeling errors can compromise the reliability of ML predictions, highlighting the need for effective uncertainty awareness to enhance prediction robustness. This paper presents a comprehensive review on navigating uncertainties in ML, categorizing uncertainty-aware approaches into probabilistic methods (including Bayesian and frequentist perspectives) and non-probabilistic methods (such as interval learning and fuzzy learning). Bayesian neural networks, known for their uncertainty quantification and nonlinear mapping capabilities, are emphasized for their superior performance and potential. The review covers various techniques and methodologies for addressing uncertainties in ML, discussing fundamentals and implementation procedures of each method. While providing a concise overview of fundamental concepts, the paper refrains from in-depth critical explanations. Strengths and limitations of each approach are examined, along with their applications in structural dynamic forward problems like response prediction, sensitivity assessment, and reliability analysis, and inverse problems like system identification, model updating, and damage identification. Additionally, the review identifies research gaps and suggests future directions for investigations, aiming to provide comprehensive insights to the research community. By offering an extensive overview of both probabilistic and non-probabilistic approaches, this review aims to assist researchers and practitioners in making informed decisions when utilizing ML techniques to address uncertainties in structural dynamic problems. Comments: 128 pages, 25 figures, 6 tables, references added Subjects: Machine Learning (cs.LG) ; Dynamical Systems (math.DS) Cite as: arXiv:2408.08629 [cs.LG] (or arXiv:2408.08629v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2408.08629 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Yan, WJ., Mei, LF., Mo, J. et al. Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Survey of Probabilistic and Non-Probabilistic Approaches. Arch Computat Methods Eng (2026) Related DOI : https://doi.org/10.1007/s11831-026-10688-3 Focus to learn more DOI(s) linking to related resources Submission history From: Linfeng Mei [ view email ] [v1] Fri, 16 Aug 2024 09:43:01 UTC (3,929 KB) [v2] Sun, 19 Oct 2025 04:26:20 UTC (3,564 KB) Full-text links: Access Paper: View PDF view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2024-08 Change to browse by: cs math math.DS References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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