Large scale variable fidelity surrogate modeling

Abstract

Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples generated by a high fidelity function (an expensive and accurate representation of a physical phenomenon) and a low fidelity function (a cheap and coarse approximation of the same physical phenomenon) while constructing a surrogate model. However, if samples sizes are more than few thousands of points, computational costs of the Gaussian process regression become prohibitive both in case of learning and in case of prediction calculation. We propose two approaches to circumvent this computational burden: one approach is based on the Nyström approximation of sample covariance matrices and another is based on an intelligent usage of a blackbox that can evaluate a low fidelity function on the fly at any point of a design space. We examine performance of the proposed approaches using a number of artificial and real problems, including engineering optimization of a rotating disk shape.

Gaussian process classification for variable fidelity data

“…Finally, in order to make our method applicable to a wide range of real projects, its scalability should be improved. A number of approaches to do this has been recently reviewed [8,41].…”

“…Gaussian process regression for multi-fidelity data has been thoroughly studied in recent years [7,8], however multi-fidelity classification based on Gaussian processes has been left behind until recently. For example, the work about feasibility regions for aeroelastic stability modeling [9] pointed out that multi-fidelity methods had been limited to continuous response models.…”

Rare Failure Prediction via Event Matching for Aerospace Applications

“…As a dependence measure we use a simple Pearson correlation, or more complex non-linear measures like mutual information; 2. For each group of parameters we use anomaly detection algorithms to detect anomalies: -The most typical anomaly detection algorithms are based on manifold modeling approaches [31]- [34]; yet another approach could be to construct a surrogate model [35]- [39] in order to approximate dependencies between the observed parameters and then detect anomalies based on a predictive error with a non-parametric confidence measure [40], [41] as the diagnostic indicator; -In a linear case we can use the low rank linear PCA reconstruction error [42] as the diagnostic timeseries; -Observations with errors, exceeding 90%-95% empirical quantile, are considered as anomalies. 3.…”

Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models

“…Gaussian Process (GP) emulators are particularly suited to be used in conjunction with multi-fidelity frameworks (Zaytsev and Burnaev, 2017). In the field of large-scale groundwater modeling Cui et al…”