Uncertainty Quantification: Latest Advances and Applications

Dear Colleagues,

Uncertainty is ubiquitous in science and engineering, which may arise from an imperfect state of knowledge or from the inherent randomness of natural phenomena such as material properties, loading conditions, and measurements. Uncertainty quantification is the process of quantitatively characterizing significant uncertainties in a complex system and of assessing their effect on computed or experimental results. Uncertainty quantification plays a vital role in reducing the risks associated with uncertainties and enhancing the fidelity of prediction in engineering design and decision making. As this is the study of mathematical models and numerical methods advances, several algorithms of uncertainty quantification are put forward, including analytic reliability methods, Monte Carlo simulation (MCs), perturbation methods, polynomial chaos expansions, the Gaussian process, etc. Despite its theoretical and practical importance, a number of open questions still exist due to the complexity of modeling, simulation, and experiments in uncertainty quantification. Hence, advances should be made to deepen our understanding in this research field.

The aim of this Special Issue is to bring together original research articles and review articles highlighting recent advances in theoretical modeling, numerical simulation, and experiments in uncertainty quantification. We also encourage submissions that investigate interesting applications involving uncertainty quantification. Research integrating machine learning or data-driven techniques is particularly welcome.

Potential topics include but are not limited to the following:

• Data-driven and machine learning techniques in uncertainty quantification.
• Novel theory of modeling uncertainty problems.
• Numerical algorithms for alleviating computational burden and/or enhancing accuracy in uncertainty quantification.
• Sensitivity analysis and optimization based on uncertainty quantification.
• Novel experimental techniques related to uncertainty quantification.
• Case studies or advanced applications of uncertainty quantification in engineering and social science.

Dr. Chensen Ding
Dr. Xiaoxiao Du
Dr. Mengxi Zhang
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• uncertainty quantification
• data-driven and machine learning
• sensitivity analysis and optimization
• uncertainty quantization experiment
• stochastic systems
• modeling and simulation
• numerical methods