Surrogate modeling of advanced computer simulations using deep Gaussian processes

Majdi I. Radaideh, Tomasz Kozlowski

Research output: Contribution to journalArticlepeer-review


The continuous advancements in computer power and computational modeling through high-fidelity and multiphysics simulations add more challenges on assessing their predictive capability. In this work, metamodeling or surrogate modeling through deep Gaussian processes (DeepGP) is performed to construct surrogates of advanced computer simulations drawn from the nuclear engineering area. This work is centered around three major ideas: (1) surrogate modeling through deep Gaussian processes (DeepGP), (2) simulation assessment through surrogate-based uncertainty quantification (UQ) methodologies, and (3) drawing conclusions regarding the underlying uncertainty of the four simulations considered in this paper. First, DeepGP models are trained, optimized, and validated to yield variety of features: (1) achieving high accuracy (small error metrics) on the validation set, (2) automatically capturing the surrogate model uncertainty (i.e. interpolation errors), (3) fitting multiple outputs with different scales simultaneously, (4) handling high dimensional input spaces, and (5) learning from small data amounts. Second, the validated DeepGP surrogates are utilized to efficiently perform UQ tasks such as uncertainty propagation (through Monte Carlo sampling), parameter screening (through Morris screening), and variance decomposition (through Sobol Indices) to investigate the selected simulations. Third, the thermal-hydraulics (fluid flow) results demonstrate the importance of inlet temperature uncertainty in void fraction predictions. For the reactor physics application (fuel depletion/consumption), DeepGP accurately captures the uncertainty in criticality calculations, which is about 0.6% (i.e. a considerable value for this application). For the application of kinetic parameters (nuclear data), DeepGP successfully explains 95% or more of the variance in all 12 outputs. Finally, DeepGP-based UQ analysis of the fuel performance application (materials science) shows the importance of the clad surface temperature, fuel porosity, and linear heat rate in explaining the variance of the maximum fuel centerline and surface temperatures.

Original languageEnglish (US)
Article number106731
JournalReliability Engineering and System Safety
StatePublished - Mar 2020


  • Bayesian learning
  • Deep GP
  • Gaussian processes
  • Nuclear reactor safety
  • Nuclear simulations
  • Uncertainty quantification

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


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