ABSTRACT
The Sparse Grids Matlab Kit (SGMK) is a software package for efficient approximation of high-dimensional models, with a focus on surrogate-based uncertainty quantification (UQ). It enables the construction of accurate surrogate models from a limited number of simulations, making it particularly suitable for applications involving computationally expensive solvers.
In this seminar, we introduce the main concepts of sparse grid methods and demonstrate their implementation within the SGMK. After a brief overview of the underlying principles, we show how sparse grids are constructed and used in practice to perform key UQ tasks. We also highlight features that make the SGMK suitable for realistic engineering workflows, such as its non-intrusive design, compatibility with existing simulation codes, and integration with external software, enabling its use in complex computational pipelines.
References
[1] C. Piazzola and L. Tamellini. The Sparse Grids Matlab Kit. https://github.com/lorenzo-tamellini/sparse-grids-matlab-kit.
[2] C. Piazzola and L. Tamellini. The Sparse Grids Matlab Kit. https://sites.google.com/view/sparse-grids-kit.
[3] C. Piazzola and L. Tamellini. Algorithm 1040: The Sparse Grids Matlab Kit – a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification. ACM Trans. Math. Softw., 50(1):1–22, 2024. doi:10.1145/3630023.
SPEAKER
Dr Chiara Piazzola is a postdoctoral researcher at the Department of Mathematics at the Technical University of Munich. She obtained her PhD in 2019 from the University of Innsbruck and held a postdoctoral position at CNR-IMATI (Pavia, Italy). Her research lies at the interface of uncertainty quantification, high-dimensional approximation, and dynamical systems, with a focus on surrogate modeling for complex computational models in engineering and environmental sciences. She is a co-developer of the Sparse Grids Matlab Kit.