Estimation of an improved surrogate model in uncertainty quantification by neural networks

DOI10.1007/s10463-020-00748-1zbMath1469.62354OpenAlexW3007104492MaRDI QIDQ2042433

Sebastian Kersting, Michael Kohler, Benedict Götz

Publication date: 20 July 2021

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10463-020-00748-1

zbMATH Keywords

neural networksdensity estimationcurse of dimensionalityuncertainty quantificationsurrogate modelsimperfect models\(L_1\) error

Mathematics Subject Classification ID

Density estimation (62G07) Applications of statistics in engineering and industry; control charts (62P30) Neural nets and related approaches to inference from stochastic processes (62M45)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Structural reliability. Statistical learning perspectives.
• Efficient calibration for imperfect computer models
• Additive regression and other nonparametric models
• The design and analysis of computer experiments.
• A distribution-free theory of nonparametric regression
• Reliability-based structural optimization using neural networks and Monte Carlo simulation
• Nonparametric regression using deep neural networks with ReLU activation function
• On deep learning as a remedy for the curse of dimensionality in nonparametric regression
• Computer model validation with functional output
• Bayesian Calibration of Computer Models
• Adaptive Density Estimation From Data With Small Measurement Errors
• Estimation of a Density Using Real and Artificial Data
• Remarks on Some Nonparametric Estimates of a Density Function
• Estimation of a density in a simulation model
• Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach
• Neural Network Learning
• Adaptive density estimation based on real and artificial data
• Nonparametric Regression Based on Hierarchical Interaction Models
• A Frequentist Approach to Computer Model Calibration
• On Estimation of a Probability Density Function and Mode