Regression Modeling for Computer Model Validation With Functional Responses

2008 ◽  
Author(s):  
Xuyuan Liu ◽  
Kwok-Leung Tsui ◽  
Wei Chen
Keyword(s):  
Computer Model ◽  
Functional Data ◽  
Single Step ◽  
Functional Regression ◽  
Computationally Efficient ◽  
Functional Responses ◽  
Physical Experiments ◽  
Step Procedure ◽  
Combining Data ◽  
Bias Function

Statistical analysis of functional responses based on functional data from both computer and physical experiments has gained increasing attention due to the dynamic nature of many engineering systems. However, the complexity and huge amount of functional data bring many difficulties to apply traditional or existing methodologies. The objective of the present study is twofold: (1) prediction of functional responses based on functional data and (2) prediction of bias function for validation of a computer model that predicts functional responses. In this paper, we first develop a functional regression model with linear basis functions to analyze functional data. Then combining data from both computer and physical experiments, we use the functional analysis modeling to predict the bias function which is crucial for validating a computer model. The proposed method, following the classical nonparametric regression framework, uses a single step procedure which is easily implemented and computationally efficient. Through an application example of motor engine analysis to predict acceleration performance and gear shift events, we demonstrate our approach and compare it to using the Gaussian process modeling approach.

Model Validation of Functional Responses Across Experimental Regions Using Functional Regression Extensions to the CORA Objective Rating System

2017 ◽  
Vol 2 (4) ◽  
Author(s):  
Scott M. Storm ◽  
Raymond R. Hill ◽  
Joseph J. Pignatiello ◽  
G. Geoffrey Vining ◽  
Edward D. White
Keyword(s):  
Functional Data ◽  
Rating System ◽  
System Response ◽  
Functional Regression ◽  
Response Functions ◽  
Weighted Linear Combination ◽  
Functional Responses ◽  
Parameter Configuration ◽  
Objective Rating ◽  
The Individual

As we continue to model more complex systems, the validation of dynamical responses has come to the forefront of modeling and simulation. One form of dynamic response is when the output is a function of time. The proper evaluation of functional data over an array of desired input parameters is critical to achieving a robust validation assessment of a simulation model. We extend the correlation analysis (CORA) objective rating system to validate functional data across experimental regions. Functional regression analysis is used to generate surrogate estimations of the system response functions at points within the region where experimental observations are absent. These CORA scores provide a measure of disagreement at each desired parameter configuration. An overall score for model validity is achieved using a weighted linear combination of the individual CORA scores. Finally, an improved CORA size scoring metric is introduced.

scholarly journals A general framework for functional regression modelling

2017 ◽  
Vol 17 (1-2) ◽  
pp. 1-35 ◽  
Author(s):  
Sonja Greven ◽  
Fabian Scheipl
Keyword(s):  
Functional Data ◽  
Regression Models ◽  
Generalized Additive Models ◽  
Large Body ◽  
Imaging Study ◽  
Additive Models ◽  
Gradient Boosting ◽  
Functional Regression ◽  
Functional Responses ◽  
Additive Mixed Models

Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for ‘generalized’ functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases—particularly splines and functional principal components—and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost , respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

A Design-Driven Validation Approach Using Bayesian Prediction Models

2007 ◽  
Vol 130 (2) ◽  
Author(s):  
Wei Chen ◽  
Ying Xiong ◽  
Kwok-Leung Tsui ◽  
Shuchun Wang
Keyword(s):  
Prediction Model ◽  
Computer Model ◽  
Bayesian Approach ◽  
Prediction Models ◽  
Bayesian Prediction ◽  
Good Resolution ◽  
Validation Metrics ◽  
Physical Experiments ◽  
Combining Data ◽  
Work Model

In most of the existing work, model validation is viewed as verifying the model accuracy, measured by the agreement between computational and experimental results. Due to the lack of resource, accuracy can only be assessed at very limited test points. However, from the design perspective, a good model should be considered the one that can provide the discrimination (with good resolution) between competing design candidates under uncertainty. In this work, a design-driven validation approach is presented. By combining data from both physical experiments and the computer model, a Bayesian approach is employed to develop a prediction model as the replacement of the original computer model for the purpose of design. Based on the uncertainty quantification with the Bayesian prediction and, subsequently, that of a design objective, some decision validation metrics are further developed to assess the confidence of using the Bayesian prediction model in making a specific design choice. We demonstrate that the Bayesian approach provides a flexible framework for drawing inferences for predictions in the intended, but maybe untested, design domain. The applicability of the proposed decision validation metrics is examined for designs with either a discrete or continuous set of design alternatives. The approach is demonstrated through an illustrative example of a robust engine piston design.

scholarly journals Wildfires Vegetation Recovery through Satellite Remote Sensing and Functional Data Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1305
Author(s):  
Feliu Serra-Burriel ◽  
Pedro Delicado ◽  
Fernando M. Cucchietti
Keyword(s):  
Remote Sensing ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Vegetation Index ◽  
Vegetation Recovery ◽  
Functional Responses ◽  
Elapsed Time ◽  
Synthetic Controls ◽  
Available Information

In recent years, wildfires have caused havoc across the world, which are especially aggravated in certain regions due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following years. We aim to explain the dynamics of wildfires’ effects on a vegetation index (previously estimated by causal inference through synthetic controls) from pre-wildfire available information (mainly proceeding from satellites). For this purpose, we use regression models from Functional Data Analysis, where wildfire effects are considered functional responses, depending on elapsed time after each wildfire, while pre-wildfire information acts as scalar covariates. Our main findings show that vegetation recovery after wildfires is a slow process, affected by many pre-wildfire conditions, among which the richness and diversity of vegetation is one of the best predictors for the recovery.

Kernel Regression Estimation for Functional Data

2018 ◽  
Author(s):  
Frédéric Ferraty ◽  
Philippe Vieu
Keyword(s):  
Kernel Methods ◽  
Functional Data ◽  
Linear Functional ◽  
Kernel Smoothing ◽  
Kernel Regression ◽  
Functional Regression ◽  
Regression Estimation ◽  
Asymptotic Results ◽  
Kernel Regression Estimation ◽  
The Impact

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.

Simultaneous Bayesian calibration and engineering design with an application to a vibration isolation system

2021 ◽  
Author(s):  
Carl Ehrett ◽  
D. Andrew Brown ◽  
Christopher Kitchens ◽  
Xinyue Xu ◽  
Roland Platz ◽  
...  
Keyword(s):  
Computer Model ◽  
Adaptive Sampling ◽  
Model Calibration ◽  
Vibration Isolation ◽  
Traditional Approach ◽  
Design Procedure ◽  
Parameter Estimates ◽  
Computationally Efficient ◽  
Isolation System ◽  
Vibration Isolation System

Abstract Calibration of computer models and the use of those models for design are two activities traditionally carried out separately. This paper generalizes existing Bayesian inverse analysis approaches for computer model calibration to present a methodology combining calibration and design in a unified Bayesian framework. This provides a computationally efficient means to undertake both tasks while quantifying all relevant sources of uncertainty. Specifically, compared with the traditional approach of design using parameter estimates from previously completed model calibration, this generalized framework inherently includes uncertainty from the calibration process in the design procedure. We demonstrate our approach on the design of a vibration isolation system. We also demonstrate how, when adaptive sampling of the phenomenon of interest is possible, the proposed framework may select new sampling locations using both available real observations and the computer model. This is especially useful when a misspecified model fails to reflect that the calibration parameter is functionally dependent upon the design inputs to be optimized.

Multiple Boris solvers for particle-in-cell (PIC) simulation

2021 ◽  
Author(s):  
Seiji Zenitani ◽  
Tsunehiko Kato
Keyword(s):  
Plasma Physics ◽  
Particle Motion ◽  
Charged Particles ◽  
Single Step ◽  
Pic Simulation ◽  
Particle In Cell ◽  
Step Procedure ◽  
Cell Simulation ◽  
Continuous Demand

<div> <div> <div> <p> Particle-in-cell (PIC) simulation has long been used in theoretical plasma physics. In PIC simulation, the Boris solver is the de-facto standard for solving particle motion, and it has been used over a half century. Meanwhile, there is a continuous demand for better particle solvers. In this contribution, we introduce a family of Boris-type schemes for integrating the motion of charged particles. We call the new solvers the multiple Boris solvers. The new solvers essentially repeat the standard two-step procedure multiple times in the Lorentz-force part, and we derive a single-step form for arbitrary subcycle number <em>n</em>. The new solvers give <em>n<sup>2</sup></em> times smaller errors, allow larger timesteps, but they are computationally affordable for moderate <em>n</em>. The multiple Boris solvers also reduce a numerical error in long-term plasma motion in a relativistic magnetized flow.</p> </div> </div> </div><p>Reference:</p><ul><li>S. Zenitani & T. N. Kato, <em>Multiple Boris integrators for particle-in-cell simulation</em>, Comput. Phys. Commun. <strong>247</strong>, 106954, doi:10.1016/j.cpc.2019.106954 (2020)</li> </ul>

scholarly journals Safety of Single Stage Revision Laparoscopic Sleeve Gastrectomy Compared to Laparoscopic Roux-Y Gastric Bypass after Failed Gastric Banding

2020 ◽  
Author(s):  
Michał Janik ◽  
Christopher Ibikunle ◽  
Ahad Khan ◽  
Amir H. Aryaie
Keyword(s):  
Gastric Bypass ◽  
Sleeve Gastrectomy ◽  
Gastric Banding ◽  
Laparoscopic Sleeve Gastrectomy ◽  
Revisional Surgery ◽  
Perioperative Complications ◽  
Single Step ◽  
Single Stage ◽  
Step Procedure ◽  
User File

Abstract Background Reoperation, after failed gastric banding, is a controversial topic. A common approach is band removal with conversion to laparoscopic Roux-Y gastric bypass (LRYGB) or laparoscopic sleeve gastrectomy (LSG) in a single-step procedure. Objective This study aimed to assess the safety of revisional surgery to LSG compared to LRYGB after failed laparoscopic adjustable gastric banding (LAGB) based on MBSAQIP Participant User File from 2015 to 2018. Methods Patients who underwent a one-stage conversion of LAGB to LSG (Conv-LSG) or LRYGB (Conv-LRYGB) were identified in the MBSAQIP PUF from 2015 to 2017. Conv-LRYGB cases were matched (1:1) with Conv-LSG patients using propensity scoring to control for potential confounding. The primary outcome was all-cause mortality. Results A total of 9974 patients (4987 matched pairs) were included in the study. Conv-LRYGB, as compared with conv-SG, was associated with a similar risk of mortality (0.02% vs. 0.06%; relative risk [RR], 0.33; 95% confidence interval [CI], 0.03 to 3.20, p = 0.32). Conversion to LRYGB increased the risk for readmission (6.16% vs. 3.77%; RR, 1.63; 95%CI, 1.37 to 1.94, p < 0.01); reoperation (2.15% vs. 1.36%; RR, 1.57; 95%CI, 1.17 to 2.12, p = <0.01); leak (1.76% vs. 1.02%; RR, 1.57; 95%CI, 1.72 to 2.42, p < 0.01); and bleeding (1.66% vs. 1.00%; RR, 1.66; 95%CI, 1.7 to 2.34, p < 0.01). Conclusions The study shows that single-stage LRYGB and LSG as revisional surgery after gastric banding, are safe in the 30-day observation with an acceptable complication rate and low mortality. However, conversion to LRYGB increased the risk of perioperative complications.

Tailor-made high porosity VOC oxidation catalysts prepared by a single-step procedure

2007 ◽  
Vol 73 (1-2) ◽  
pp. 128-134 ◽  
Author(s):  
J. Blanco ◽  
A.L. Petre ◽  
M. Yates ◽  
M.P. Martin ◽  
J.A. Martin ◽  
...  
Keyword(s):  
Single Step ◽  
High Porosity ◽  
Oxidation Catalysts ◽  
Voc Oxidation ◽  
Step Procedure
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