scholarly journals Uncertainty analysis of deterministic models with gaussian process approximation

2016 ◽  
pp. 1-20
Author(s):  
Rustem Shainurovich Kalmetiev ◽  
Yurii Nikolaevich Orlov
Keyword(s):  
Uncertainty Analysis ◽  
Gaussian Process ◽  
Deterministic Models ◽  
Process Approximation

scholarly journals Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions

2018 ◽  
Vol 30 (11) ◽  
pp. 3072-3094 ◽  
Author(s):  
Hongqiao Wang ◽  
Jinglai Li
Keyword(s):  
Bayesian Inference ◽  
Gaussian Process ◽  
Adaptive Algorithm ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
Inference Problems ◽  
Active Learning Method ◽  
Computationally Intensive ◽  
Process Approximation

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP)–based method to approximate the joint distribution of the unknown parameters and the data, built on recent work (Kandasamy, Schneider, & Póczos, 2015 ). In particular, we write the joint density approximately as a product of an approximate posterior density and an exponentiated GP surrogate. We then provide an adaptive algorithm to construct such an approximation, where an active learning method is used to choose the design points. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for Bayesian computation.

Frequency Response-Based Uncertainty Analysis of Vibration System Utilizing Multiple Response Gaussian Process

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Wangbai Pan ◽  
Guoan Tang ◽  
Jiong Tang
Keyword(s):  
Uncertainty Analysis ◽  
Gaussian Process ◽  
Frequency Response ◽  
Model Updating ◽  
Uncertainty Propagation ◽  
Multiple Response ◽  
Vibration System ◽  
Vector Fitting ◽  
Fitting Method ◽  
Small Set

This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification.

scholarly journals Sensitivity and uncertainty analysis of two human atrial cardiac cell models using Gaussian process emulators

2019 ◽  
Author(s):  
Sam Coveney ◽  
Richard H. Clayton
Keyword(s):  
Cell Membrane ◽  
Action Potential ◽  
Uncertainty Analysis ◽  
Gaussian Process ◽  
Model Parameters ◽  
Cardiac Cell ◽  
Cell Models ◽  
First Order ◽  
Sensitivity Indices ◽  
Sensitivity And Uncertainty Analysis

AbstractCardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes, and are becoming widely used research tools. These models are highly detailed, with many parameters in the equations that describe current flow through ion channels, pumps, and exchangers in the cell membrane, and so it is difficult to link changes in model inputs to model behaviours. The aim of the present study was to undertake sensitivity and uncertainty analysis of two models of the human atrial action potential. We used Gaussian processes to emulate the way that 11 features of the action potential and calcium transient produced by each model depended on a set of. The emulators were trained by maximising likelihood conditional on a set of design data, obtained from 300 model evaluations. For each model evaluation, the set of inputs was obtained from uniform distributions centred on the default values for each parameter, using latin-hypercube sampling. First order and total effect sensitivity indices were calculated for each combination of input and output. First order indices were well correlated with the square root of sensitivity indices obtained by partial least squares regression of the design data. The sensitivity indices highlighted a difference in the balance of inward and outward currents during the plateau phase of the action potential in each model, with the consequence that changes to one parameter can have opposite effects in the two models. Overall the interactions among inputs were not as important as the first order effects, indicating that model parameters tend to have independent effects on the model outputs. This study has shown that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of cardiac cell models.Author summaryThe time course of the cardiac action potential is determined by the balance of inward and outward currents across the cell membrane, and these in turn depend on dynamic behaviour of ion channels, pumps and exchangers in the cell membrane. Cardiac cell models reconstruct the action potential by representing transmembrane current as a set of stiff and nonlinear ordinary differential equations. These models capture biophysical detail, but are complex and have large numbers of parameters, so cause and effect relationships are difficult to identify. In recent years there has been an increasing interest in uncertainty and variability in computational models, and a number of tools have been developed. In this study we have used one of these tools, Gaussian process emulators, to compare and contrast two models of the human atrial action potential. We obtained sensitivity indices based on the proportion of variance in a model output that is accounted for by variance in each of the model parameters. These sensitivity indices highlighted the model parameters that had the most influence on the model outputs, and provided a means to make a quantitative comparison between the models.

scholarly journals The Probabilistic Deconvolution of the Distribution of Relaxation Times with Finite Gaussian Processes

2021 ◽  
Author(s):  
Adeleke Maradesa ◽  
Baptiste Py ◽  
Emanuele Quattrocchi ◽  
Francesco Ciucci
Keyword(s):  
Experimental Data ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Electrochemical Impedance ◽  
Probabilistic Approach ◽  
Relaxation Times ◽  
Electrochemical Systems ◽  
Process Approximation ◽  
Machine Learning Tool ◽  
New Framework

Electrochemical impedance spectroscopy (EIS) is a tool widely used to study the properties of electrochemical systems. The distribution of relaxation times (DRT) has emerged as one of the main methods for the analysis of EIS spectra. Gaussian processes can be used to regress EIS data, quantify uncertainty, and deconvolve the DRT, but current implementations do not constrain the DRT to be positive and can only use the imaginary part of EIS spectra. Herein, we overcome both issues by using a finite Gaussian process approximation to develop a new framework called the finite Gaussian process distribution of relaxation times (fGP-DRT). The analysis on artificial EIS data shows that the fGP-DRT method consistently recovers exact DRT from noise-corrupted EIS spectra while accurately regressing experimental data. Furthermore, the fGP-DRT framework is used as a machine learning tool to provide probabilistic estimates of the impedance at unmeasured frequencies. The method is further validated against experimental data from fuel cells and batteries. In short, this work develops a novel probabilistic approach for the analysis of EIS data based on Gaussian process, opening a new stream of research for the deconvolution of DRT.

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