Toni Karvonen: Probabilistic Richardson Extrapolation скачать в хорошем качестве

Toni Karvonen: Probabilistic Richardson Extrapolation

Abstract: Richardson extrapolation is a classical technique to accelerate the rate of convergence of a numerical method. For example, Romberg's method uses Richardson extrapolation to estimate integrals and the Bulirsch–Stoer algorithm to solve ordinary differential equations. We use a probabilistic Richardson extrapolation method based on Gaussian processes that unifies classical extrapolation methods with multi-fidelity modelling and handles uncertain convergence orders by allowing these to be statistically estimated. Moreover, the probabilistic formulation enables statistical experimental design. We prove that the method achieves a polynomial speed-up compared to the original numerical method and apply it to cardiac modelling. Preprint: C. J. Oates, T. Karvonen, A. L. Teckentrup, M. Strocchi & S. A. Niederer (2024). Probabilistic Richardson extrapolation. arXiv:2401.07562. Bio: Toni Karvonen has been an Associate Professor in applied mathematics at the Lappeenranta–Lahti University of Technology LUT since September 2024. He obtained an MSc in applied mathematics from the University of Helsinki in 2015 and a doctoral degree in electrical engineering from Aalto University in 2019. In 2020–21 he was a Research Fellow at the Alan Turing Institute, the UK's national institute for data science and AI located in London, and in 2021–24 an Academy Postdoctoral Researcher in the Department of Mathematics and Statistics at the University of Helsinki. His research focuses on uncertainty quantification and model misspecification in numerical analysis, statistical modelling, and machine learning.