Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 473; no. 2198; p. 20160751
• Main Authors: Perdikaris, P., Raissi, M., Damianou, A., Lawrence, N. D., Karniadakis, G. E.
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 01.02.2017
• Edition: Royal Society (Great Britain)
• Subjects: Algorithms; Autoregressive processes; Bayesian Inference; Complexity; Computational fluid dynamics; Computer simulation; Correlation; Data integration; Deep Learning; Gaussian distribution; Gaussian process; Gaussian Processes; Multisensor fusion; Statistical analysis; Trends; Uncertainty Quantification; deep learning; uncertainty quantification; Bayesian inference; Gaussian processes
• ISSN: 1364-5021; 1471-2946; 1471-2946
• DOI: 10.1098/rspa.2016.0751

Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.