A Gaussian Process Emulator Based Approach for Bayesian Calibration of a Functional Input

Technometrics ◽  
2021 ◽  
pp. 1-21
Author(s):  
Zhaohui Li ◽  
Matthias Hwai Yong Tan
Keyword(s):  
Gaussian Process ◽  
Bayesian Calibration ◽  
Gaussian Process Emulator

scholarly journals Probabilistic Power Flow Based on a Gaussian Process Emulator

2020 ◽  
Vol 35 (4) ◽  
pp. 3278-3281 ◽  
Author(s):  
Yijun Xu ◽  
Zhixiong Hu ◽  
Lamine Mili ◽  
Mert Korkali ◽  
Xiao Chen
Keyword(s):  
Gaussian Process ◽  
Power Flow ◽  
Probabilistic Power Flow ◽  
Gaussian Process Emulator

scholarly journals Bayesian Sensitivity Analysis of a Cardiac Cell Model Using a Gaussian Process Emulator

PLoS ONE ◽  
2015 ◽  
Vol 10 (6) ◽  
pp. e0130252 ◽  
Author(s):  
Eugene T Y Chang ◽  
Mark Strong ◽  
Richard H Clayton
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Cell Model ◽  
Cardiac Cell ◽  
Gaussian Process Emulator

scholarly journals Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters

2011 ◽  
Vol 11 (7) ◽  
pp. 20433-20485 ◽  
Author(s):  
L. A. Lee ◽  
K. S. Carslaw ◽  
K. Pringle ◽  
G. W. Mann ◽  
D. V. Spracklen
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Interaction Effects ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Model Output ◽  
Aerosol Model ◽  
Uncertainty Space ◽  
Gaussian Process Emulation ◽  
Gaussian Process Emulator

Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric model.

A Gaussian process emulator for simulating ice sheet-climate interactions on a multi-million year timescale

2020 ◽  
Author(s):  
Jonas Van Breedam ◽  
Philippe Huybrechts ◽  
Michel Crucifix
Keyword(s):  
Gaussian Process ◽  
Climate Model ◽  
Ice Sheet ◽  
Climate System ◽  
Lapse Rate ◽  
Coupled Models ◽  
Climate Interactions ◽  
Coupling Time ◽  
Fully Coupled ◽  
Gaussian Process Emulator

<p>Fully coupled state-of-the-art Atmosphere-Ocean General Circulation Models are the best tool to investigate feedbacks between the different components of the climate system on a decadal to centennial timescale. On millennial to multi-millennial timescales, Earth System Models of Intermediate Complexity are used to explore the feedbacks in the climate system between the ice sheets, the atmosphere and the ocean. Those fully coupled models, even at coarser resolution, are computationally very expensive and other techniques have been proposed to simulate ice sheet-climate interactions on a million-year timescale. The asynchronous coupling technique proposes to run a climate model for a few decades and subsequently an ice sheet model for a few millennia. Another, more efficient method is the use of a matrix look-up table where climate model runs are performed for end-members and intermediate climatic states are linearly interpolated.</p><p>In this study, a novel coupling approach is presented where a Gaussian Process emulator applied to the climate model HadSM3 is coupled to the ice sheet model AISMPALEO. We have tested the sensitivity of the formulation of the ice sheet parameter and of the coupling time to the evolution of the ice sheet over time. Additionally, we used different lapse rate adjustments between the relatively coarse climate model and the much finer ice sheet model topography. It is shown that the ice sheet evolution over a million year timescale is strongly sensitive to the choice of the coupling time and to the implementation of the lapse rate adjustment. With the new coupling procedure, we provide a more realistic and computationally efficient framework for ice sheet-climate interactions on a multi-million year timescale.</p><p> </p>

scholarly journals Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters

2011 ◽  
Vol 11 (23) ◽  
pp. 12253-12273 ◽  
Author(s):  
L. A. Lee ◽  
K. S. Carslaw ◽  
K. J. Pringle ◽  
G. W. Mann ◽  
D. V. Spracklen
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Interaction Effects ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Model Output ◽  
Atmospheric Models ◽  
Aerosol Model ◽  
Gaussian Process Emulation ◽  
Gaussian Process Emulator

Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity through comparison of driving processes, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space, using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric models.

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

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 53
Author(s):  
Yun Am Seo ◽  
Jeong-Soo Park
Keyword(s):  
Iterative Method ◽  
Gaussian Process ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Tuning Parameters ◽  
Squared Error ◽  
Model Study ◽  
Calibration Methods ◽  
Gp Model ◽  
Gaussian Process Emulator

The approximated non-linear least squares (ALS) tunes or calibrates the computer model by minimizing the squared error between the computer output and real observations by using an emulator such as a Gaussian process (GP) model. A potential defect of the ALS method is that the emulator is constructed once and it is no longer re-built. An iterative method is proposed in this study to address this difficulty. In the proposed method, the tuning parameters of the simulation model are calculated by the conditional expectation (E-step), whereas the GP parameters are updated by the maximum likelihood estimation (M-step). These EM-steps are alternately repeated until convergence by using both computer and experimental data. For comparative purposes, another iterative method (the max-min algorithm) and a likelihood-based method are considered. Five toy models are tested for a comparative analysis of these methods. According to the toy model study, both the variance and bias of the estimates obtained from the proposed EM algorithm are smaller than those from the existing calibration methods. Finally, the application to a nuclear fusion simulator is demonstrated.

scholarly journals A Gaussian Process Emulator for Estimating the Volume of Tissue Activated During Deep Brain Stimulation

2015 ◽  
pp. 691-699 ◽  
Author(s):  
Iván De La Pava ◽  
Viviana Gómez ◽  
Mauricio A. Álvarez ◽  
Óscar A. Henao ◽  
Genaro Daza-Santacoloma ◽  
...  
Keyword(s):  
Deep Brain Stimulation ◽  
Gaussian Process ◽  
Brain Stimulation ◽  
Gaussian Process Emulator ◽  
Deep Brain
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