TY - GEN

T1 - Variable fidelity regression using low fidelity function blackbox and sparsification

AU - Zaytsev, A.

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - We consider construction of surrogate models based on variable fidelity samples generated by a high fidelity function (an exact representation of some physical phenomenon) and by a low fidelity function (a coarse approximation of the exact representation). A surrogate model is constructed to replace the computationally expensive high fidelity function. For such tasks Gaussian processes are generally used. However, if the sample size reaches a few thousands points, a direct application of Gaussian process regression becomes impractical due to high computational costs. We propose two approaches to circumvent this difficulty. The first approach uses approximation of sample covariance matrices based on the Nyström method. The second approach relies on the fact that engineers often can evaluate a low fidelity function on the fly at any point using some blackbox; thus each time calculating prediction of a high fidelity function at some point, we can update the surrogate model with the low fidelity function value at this point. So, we avoid issues related to the inversion of large covariance matrices — as we can construct model using only a moderate low fidelity sample size. We applied developed methods to a real problem, dealing with an optimization of the shape of a rotating disk.

AB - We consider construction of surrogate models based on variable fidelity samples generated by a high fidelity function (an exact representation of some physical phenomenon) and by a low fidelity function (a coarse approximation of the exact representation). A surrogate model is constructed to replace the computationally expensive high fidelity function. For such tasks Gaussian processes are generally used. However, if the sample size reaches a few thousands points, a direct application of Gaussian process regression becomes impractical due to high computational costs. We propose two approaches to circumvent this difficulty. The first approach uses approximation of sample covariance matrices based on the Nyström method. The second approach relies on the fact that engineers often can evaluate a low fidelity function on the fly at any point using some blackbox; thus each time calculating prediction of a high fidelity function at some point, we can update the surrogate model with the low fidelity function value at this point. So, we avoid issues related to the inversion of large covariance matrices — as we can construct model using only a moderate low fidelity sample size. We applied developed methods to a real problem, dealing with an optimization of the shape of a rotating disk.

KW - Cokriging

KW - Gaussian process

KW - Multifidelity data

KW - Nonlinear regression

KW - Nyström approximation

UR - http://www.scopus.com/inward/record.url?scp=84964055123&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-33395-3_11

DO - 10.1007/978-3-319-33395-3_11

M3 - Conference contribution

AN - SCOPUS:84964055123

SN - 9783319333946

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 147

EP - 164

BT - Conformal and Probabilistic Prediction with Applications - 5th International Symposium, COPA 2016, Proceedings

A2 - Vega, Jesus

A2 - Gammerman, Alexander

A2 - Luo, Zhiyuan

A2 - Vovk, Vladimir

PB - Springer Verlag

T2 - 5th International Symposium on Conformal and Probabilistic Prediction with Applications, COPA 2016

Y2 - 20 April 2016 through 22 April 2016

ER -