2019/05/23 by Philip G. Breen, Christopher N. Foley, Breen, Philip G. +1
Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1905.09892
openalex publication_date 2019/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we treat the problem of evaluating the asymptotic error in a numerical integration scheme as one with inherent uncertainty. Adding to the growing field of probabilistic numerics, we show that Gaussian process regression (GPR) can be embedded into a numerical integration scheme to allow for (i) robust selection of the adaptive step-size parameter and; (ii) uncertainty quantification in predictions of putatively converged numerical solutions. We present two examples of our approach using Richardson's extrapolation technique and the Bulirsch-Stoer algorithm. In scenarios where the error-surface is smooth and bounded, our proposed approach can match the results of the traditional polynomial (parametric) extrapolation methods. In scenarios where the error surface is not well approximated by a finite-order polynomial, e.g. in the vicinity of a pole or in the assessment of a chaotic system, traditional methods can fail, however, the non-parametric GPR approach demonstrates the potential to continue to furnish reasonable solutions in these situations.