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Expectation-Maximization Algorithm for the Calibration of Complex Simulator Using a Gaussian Process Emulator.

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Summary
This summary is machine-generated.

This study introduces an iterative Expectation-Maximization (EM) algorithm for calibrating computer models, improving upon approximated non-linear least squares (ALS) by iteratively updating parameters. The EM algorithm demonstrates reduced variance and bias in model estimates compared to existing methods.

Keywords:
Latin-hypercube designbest linear unbiased predictorcode tuningiterative algorithmmean squared errormetamodelnumerical optimizationsurrogate

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Area of Science:

  • Computational modeling and simulation
  • Statistical inference and machine learning

Background:

  • Approximated non-linear least squares (ALS) calibrates models using Gaussian process (GP) emulators, but emulators are built only once.
  • This static approach can limit the accuracy and adaptability of model calibration.

Purpose of the Study:

  • To develop an iterative method for computer model calibration that addresses the limitations of static emulator construction.
  • To enhance the accuracy and reliability of model tuning by incorporating iterative updates.

Main Methods:

  • An iterative Expectation-Maximization (EM) algorithm is proposed, alternating between E-steps (calculating tuning parameters) and M-steps (updating GP parameters).
  • The method utilizes both computer simulation outputs and experimental data for iterative refinement until convergence.
  • Comparative analysis includes the max-min algorithm and a likelihood-based method.

Main Results:

  • The proposed EM algorithm showed smaller variance and bias in parameter estimates compared to existing calibration methods in toy model studies.
  • Demonstrated successful application to a complex nuclear fusion simulator, validating its practical utility.

Conclusions:

  • The iterative EM algorithm offers a more robust and accurate approach to computer model calibration than traditional static methods.
  • This iterative strategy enhances the precision of simulation models by continuously refining emulator parameters.