Efficient numerical methods to deal with imprecise probabilities
Matthias G. R. Faes
Numerical tools to approximate the solution of (sets of) differential equations have become indispensable in the design of components from the micro-scale to complete structures. Thanks to these tools, an engineer is now able to design, test and optimize designs long before a first prototype is built. However, despite the highly detailed numerical predictions that can be obtained, the results of these calculations often show a non-negligible discrepancy with the actual physical behavior of the structure. At the core of this discrepancy lies uncertainty in the description of the model physics, as well as the governing parameters.
Uncertainties are especially commonly encountered in the context of structural dynamics, where for instance the effect natural phenomena such as earthquakes or wind loads on structures has to be considered. Indeed, due to the sheer complexity of the underlying physics, the corresponding dynamical loads that act on the system often cannot be described in a crisp way. Stochastic processes provide a rigorous framework to deal with the uncertainties and space/time correlations of uncertain loads by resorting to the well-documented framework of probability theory. However, in practice, the analyst is often confronted with limited, incomplete or conflicting sources of data (i.e., epistemic uncertainty). In this case, the application of a pure probabilistic framework to take this additional level of uncertainty into account is questionable since in this case, there is simply not enough information to construct an objective probabilistic uncertainty model.
In this research seminar, I will talk about how to deal with this challenging problem of modelling uncertainties in space and/or time under limited data. More precisely, I will show how to define and model imprecise stochastic processes that are robust with respect to missing and/or conflicting data, as well as present some efficient methodologies to effectively propagate these processes through numerical simulation models.
About the speaker
Matthias Faes became a full Professor in Reliability Engineering at TU Dortmund at the age of 30, since February 2022. Before, he was a post-doctoral fellow of the Research Foundation Flanders (FWO) working at the Department of Mechanical Engineering of KU Leuven, and was also affiliated to the Institute for Risk and Reliability at the University of Hannover as Humboldt Fellow. He graduated summa cum laude as Master of Science in Engineering Technology in 2013 and obtained his PhD in Engineering Technology from KU Leuven in 2017. Since then, he is working on advanced methodologies for non-probabilistic uncertainty quantification under scarce data and information, including inverse and data-driven methods, stochastic fields and interval techniques. He is a Laureate of the 2017 PhD award of the Belgian National Committee for Applied and Theoretical Mechanics, winner of the 2017 ECCOMAS European PhD award for best PhD thesis in 2017 on computational methods in applied sciences and engineering in Europe, winner of the 2019 ISIPTA - IJAR Young Researcher Award for outstanding contributions to research on imprecise probabilities and the 2023 EASD Junior Research Prize for his contribution to the development of methodologies for structural dynamics, among other awards. He is editor at Mechanical Systems and Signal Processing and Associate Managing Editor of the ASCE-ASME Journal of Risk and Uncertainty in Engineering system parts A and B, among other journals. Matthias Faes is author of more than 60 journal papers and more than 60 conference contributions and he has a Google Scholar H-index of 20 (1600+ citations) since 2016.