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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

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Generalized Nonlinear Least Squares Method for the Calibration of Complex Computer Code Using a Gaussian Process

Youngsaeng Lee^1,2, Jeong-Soo Park²

¹Data Science Lab, Korea Electric Power Corporation, Seoul 60732, Korea.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

The new generalized approximated nonlinear least squares (GALS) and max-minG algorithms improve parameter estimation in complex computer models by addressing correlated residuals and surrogate model uncertainty. These methods offer reduced bias and variance compared to traditional approaches.

Keywords:

Kriging best linear unbiased predictor big data code tuning combined data computer experiments iteratively re-weighted least squares numerical optimization

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Area of Science:

Computational modeling
Statistical inference
Scientific computing

Background:

Approximated nonlinear least squares (ALS) is used for parameter estimation in complex, time-consuming computer codes.
ALS calibrates codes by minimizing differences between observations and model outputs using surrogates like Gaussian processes.
Correlated or heteroscedastic residuals and surrogate uncertainty can distort ALS tuning and increase estimation variance.

Purpose of the Study:

To propose a generalized approximated nonlinear least squares (GALS) method to address limitations of the standard ALS.
To introduce an iterative version of GALS, the max-minG algorithm, for enhanced parameter estimation.
To compare the performance of GALS and max-minG against ALS and iteratively re-weighted ALS (IRWALS).

Main Methods:

GALS constructs a covariance matrix for residuals, incorporating its inverse into the minimization objective.
The max-minG algorithm iteratively re-estimates parameters using maximum likelihood estimation and GALS.
Four methods (ALS, IRWALS, GALS, max-minG) were compared using five test functions and a nuclear fusion simulator.

Main Results:

Both GALS and max-minG demonstrated smaller bias and variance in parameter estimates compared to ALS and IRWALS.
The max-minG algorithm showed superior performance over GALS and other methods for complex test functions.
Proposed methods resolved abnormal residual patterns observed with the standard ALS method in a nuclear fusion simulation.

Conclusions:

The proposed GALS and max-minG algorithms offer significant improvements in parameter estimation accuracy and stability for complex computer models.
Max-minG is particularly effective for computationally intensive and complex simulation scenarios.
These advanced methods provide robust solutions for challenges posed by correlated residuals and surrogate model uncertainties in scientific computing.