RECURSIVE CO-KRIGING MODEL FOR DESIGN OF COMPUTER EXPERIMENTS WITH MULTIPLE LEVELS OF FIDELITY

By Loic Le Gratiet. 2012

369 citations recorded by the source corpus.

We consider in this paper the problem of building a fast-running approximation—also called surrogate model—of a complex computer code. The co-kriging based surrogate model is a promising tool to build such an approximation when the complex computer code can be run at different levels of accuracy. We present here an original approach to perform a multi-fidelity co-kriging model which is based on a recursive formulation. We prove that the predictive mean and the variance of the presented approach are identical to the ones of the original co-kriging model. However, our new approach allows to obtain original results. First, closed-form formulas for the universal co-kriging predictive mean and variance are given. Second, a fast cross-validation procedure for the multi-fidelity co-kriging model is introduced. Finally, the proposed approach has a reduced computational complexity compared to the previous one. The multi-fidelity model is successfully applied to emulate a hydrodynamic simulator.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6f26a7f26fd5eb8b35212a517cef0dd1fde56eff

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Citations in the corpus

Performance study of multi-fidelity gradient enhanced kriging (2015, methodology): “It is based on the recursive CoKriging model of Le Gratiet (2012). Additionally, it incorporates multi-fidelity gradient data along with multi-fidelity function data to enhance surrogate model accuracy.”
Review of multi-fidelity models (2016, background): “Accounting for these correlations can improve the model’s predictive performance, making the model more complex and computationally intensive [174, 131, 69].”
Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization (2017, methodology): “To reduce the matrix dimension and thus the computational cost, LeGratiet [21] presented a recursive multi-fidelity GPR, which allowed one to train the coupled GPRs separately.”
Recent Advances in Bayesian Optimization (2022, methodology): “To improve the computational eiciency, a recursive formulation for Co-Kriging was proposed in [103], assuming that the training datasets for ŷH (x) and ŷL (x) have a nested structure, i.”
Machine learning of linear differential equations using Gaussian processes (2017, background): “This results in the so-called recursive co-kriging [24, 25] model f(x) = φu(x)+ v(x).”
Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models (2019, methodology): “This approach has been widely used [16] and has been extended for efficiency [17] and to accommodate large data-sets [18].”
Multi-Information Source Optimization (2016, background): “In this problem, IS are supposed to form a strict hierarchy [16, 14, 6, 24, 20, 19, 15].”
Remarks on multi-output Gaussian process regression (2018, methodology): “[74] have derived that the multi-output modeling process can be decomposed into T successive and independent modeling processes, allowing to infer the hyperparameters for each output separately.”
Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets (2016, methodology): “Furthermore, the use of GPs within autoregressive stochastic models, such as the widely used scheme put forth by Kennedy and O’Hagan [4] and the efficient recursive implementation of Le Gratiet and Garnier [5], allows for exploring spatial cross-correlations between heterogeneous information sources”
Multi-fidelity Gaussian process regression for prediction of random fields (2017, background): “where ã j−1)(ξ) and z j)(ξ) are appropriate Gaussian random fields, while ρ j−1)(ξ) are deterministic scaling fields (see [15,14,13] for further details).”
A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design (2017, background): “To address the “ which ” issue, the Co-Kriging process is organized in a recursive formulation (Le Gratiet and Garnier 2014) which offers the contribution of each level of simulation to the final model.”