June 27, 2022 @ 11:00 am - 12:30 pm
Non-intrusive Polynomial Chaos Expansions: Adaptivity, Sparsity and Active Learning
Lukáš Novák, Assistant Professor, Faculty of Civil Engineering, Brno University of Technology
Attend in person: JHU Homewood campus, Malone Hall, G 33/35
Attend online via Zoom
Polynomial chaos expansion (PCE) represents a versatile tool for uncertainty quantification of mathematical models of physical systems. Although PCE is typically used only as a surrogate model of a black-box model, it also allows for analytical derivation of statistical characteristics of a given quantity of interest. A combination of computational efficiency and strong theoretical background predetermines PCE as an ideal method for industrial applications. However, the naive implementation typically leads to curse-of-dimensionality, since the number of estimated deterministic coefficients is highly dependent on the given stochastic dimension of the model and polynomial order used for the construction of PCE. The seminar is focused on the adaptivity of basis functions and sparse solutions, which dramatically reduces the computational cost of PCE construction. Since each evaluation of a computer model representing the engineering problem is typically highly time-consuming, it is necessary to further reduce the number of model evaluations as much as possible in the process of training the surrogate model, while maintaining the accuracy of the approximation. The balance between accuracy and computational requirements is strongly connected to the selection of the support points in the design domain of input random variables. It is efficient and practical to create additional samples one by one until the desired accuracy of the approximation is reached. The concept of adaptive sequential experimental design (active learning) for PCE will be discussed together with the recent research results focused on the decomposition of the design domain.
Lukáš Novák is an assistant professor at the Brno University of Technology, Faculty of Civil Engineering. He holds a Ph.D. in Structural Mechanics and a Master’s degree in Civil Engineering. His research interests lie within the field of uncertainty quantification and structural reliability. He is particularly interested in polynomial chaos expansion, sensitivity analysis, and semi-probabilistic methods for the design and assessment of concrete structures.