Year: 2024
Type: preprint
Abstract: For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of a numerical method. However, these tools are not well-suited to modern computer codes, where multiple continua are discretised and convergence orders are not easily analysed. To address this challenge we present a probabilistic perspective on Richardson extrapolation, a point of view that unifies classical extrapolation methods with modern multi-fidelity modelling, and handles uncertain convergence orders by allowing these to be statistically estimated. The approach is developed using Gaussian processes, leading to Gauss-Richardson Extrapolation (GRE). Conditions are established under which extrapolation using the conditional mean achieves a polynomial (or even an exponential) speed-up compared to the original numerical method. Further, the probabilistic formulation unlocks the possibility of experimental design, casting the selection of fidelities as a continuous optimisation problem which can then be (approximately) solved. A case-study involving a computational cardiac model demonstrates that practical gains in accuracy can be achieved using the GRE method.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1247657515, Predicting Outcome of Rate or Rhythm Control in Patients with Atrial Fibrillation and Heart Failure, G2203179303, Uncertainty Quantification in Prospective and Predictive Patient Specific Cardiac Models, G3081709163, G3341554066, Isaac Newton Institute for Mathematical Sciences, Harnessing the Power of Stein Discrepancies in Bayesian Computation, Selecting rhythm or rate control in patients with both atrial fibrillation and heart failure, The Alan Turing Institute 22/23 - Core and Additional Funding, G9000037332, G961285871
OpenAlex ID: W4391009388