Reduced order modeling for nonlinear structural analysis using Gaussian process regression
Mengwu Guo,Jan S. Hesthaven +1 more
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TLDR
A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations, and the Gaussian process regression is used to approximate the projection coefficients.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2018-11-01 and is currently open access. It has received 180 citations till now. The article focuses on the topics: Nonlinear system & Projection (linear algebra).read more
Figures
Figure 2: (a) Geometry and input parameters for a trussed frame; (b)Load-displacement curves in both hyperelastic and hyperelasto-plastic cases. 
Figure 8: Geometry and pressure loads for the twisting column 
Figure 9: Configurations of the twisting column at different loading stages 
Figure 11: Regression results for the surface of displacement uX of the labelled node B versus µ1 and µ2 
Figure 10: (a) Regression results for the curve of displacement uX of the labelled node B versus pressure load µ1 = p; (b) Prediction of uX at node B and its derivative with respect to µ1, both calculated from the GPR model trained by 28 selected samples. 
Figure 4: Predictive results by the GPR and the ANN: (a) – (e) Comparisons of predictive results by the GPR and the ANN for the 5 entries of VTuh; (f) Regression results for the load-displacement curve by both the GPR and the ANN.
Citations
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Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Journal ArticleDOI
Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
TL;DR: The proposed reduced-basis method, referred as the POD-NN, fully decouples the online stage and the high-fidelity scheme, and is thus able to provide fast and reliable solutions of complex unsteady flows.
Journal ArticleDOI
Data-driven reduced order modeling for time-dependent problems
Mengwu Guo,Jan S. Hesthaven +1 more
TL;DR: The proposed approach provides a reliable and efficient tool for approximating parametrized time-dependent problems, and its effectiveness is illustrated by non-trivial numerical examples.
Journal ArticleDOI
Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
Jiayang Xu,Karthik Duraisamy +1 more
TL;DR: The results suggest that given adequate data and careful training, effective data-driven predictive models can be constructed and evaluated on a range of problems involving discontinuities, wave propagation, strong transients, and coherent structures.
Journal ArticleDOI
A deep energy method for finite deformation hyperelasticity
TL;DR: The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch.
References
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Book
Neural Networks: A Comprehensive Foundation
TL;DR: Thorough, well-organized, and completely up to date, this book examines all the important aspects of this emerging technology, including the learning process, back-propagation learning, radial-basis function networks, self-organizing systems, modular networks, temporal processing and neurodynamics, and VLSI implementation of neural networks.
Book
Pattern Recognition and Machine Learning
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.
Book
Gaussian Processes for Machine Learning
TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Book
Finite Element Procedures
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.