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

arXiv: https://arxiv.org/abs/2408.08629 · HTML: https://mlsanity.com/paper/2408.08629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 215 references that are in the map.
- First posted on arXiv 16 Aug 2024.

## Builds on (most cited first, 21 of 21)

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- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
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- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [Learning Functional Priors and Posteriors from Data and Physics](https://mlsanity.com/paper/2106.05863/) (2021)
- [A Review of Vibration-Based Damage Detection in Civil Structures: From Traditional Methods to Machine Learning and Deep Learning Applications](https://mlsanity.com/paper/2004.04373/) (2020)
- [Maximizing Overall Diversity for Improved Uncertainty Estimates in Deep Ensembles](https://mlsanity.com/paper/1906.07380/) (2019)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Semi-supervised clustering methods](https://mlsanity.com/paper/1307.0252/) (2013)
- [A Review of Data-Driven Discovery for Dynamic Systems](https://mlsanity.com/paper/2210.10663/) (2022)
- [Active learning for structural reliability: survey, general framework and benchmark](https://mlsanity.com/paper/2106.01713/) (2021)
- [Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty](https://mlsanity.com/paper/2110.08607/) (2021)
- [Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data](https://mlsanity.com/paper/1907.04240/) (2019)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes](https://mlsanity.com/paper/2309.11875/) (2023)
- [Reliability Analysis of Complex Systems using Subset Simulations with Hamiltonian Neural Networks](https://mlsanity.com/paper/2401.05244/) (2024)

## Abstract (arXiv)

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.