A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network
TLDR
The capability of the proposed neural network-based identification method to efficiently solve the underlying statistical inverse problem is illustrated through two numerical examples developed within the framework of 2D plane stress linear elasticity.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2021-01-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Artificial neural network & Statistical model.read more
Citations
More filters
Journal ArticleDOI
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems
TL;DR: In this paper , the authors explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver.
Posted Content
Approximations of Effective Coefficients in Stochastic Homogenization
TL;DR: In this paper, the authors considered the problem of approximating homogenized coefficients of second order divergence form elliptic operators with random statistically homogeneous coefficients, by means of periodization and other cut-off procedures.
Journal ArticleDOI
Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)
TL;DR: In this article , the authors proposed the Thermodynamics-based Artificial Neural Networks (TANN) for the constitutive modeling of materials with inelastic and complex microstructure.
Journal ArticleDOI
Perspective: Machine learning in experimental solid mechanics
N.R. Brodnik,C. Muir,N. Tulshibagwale,Jeff Rossin,McLean P. Echlin,C.M. Hamel,S.L.B. Kramer,T. Pollock,James D. Kiser,C. Smith,S. Daly +10 more
TL;DR: In this paper , the authors embed physical principles into machine learning (ML) architectures to evaluate and compare ML frameworks against benchmark datasets, and to test their broader extensibility, which enables ML models with a wide range of architectures to be compared, compared, evaluated, and extended to broader experimental and computational frameworks.
Journal ArticleDOI
Computational stochastic homogenization of heterogeneous media from an elasticity random field having an uncertain spectral measure
TL;DR: In this article, a probabilistic analysis of the random effective elasticity tensor at macroscale is performed as a function of the level of spectrum uncertainties, which allows for studying the scale separation and the representative volume element size in a robust probababilistic framework.
References
More filters
Journal ArticleDOI
Maximum likelihood estimation of stochastic chaos representations from experimental data
TL;DR: In this paper, the identification of probabilistic models of the random coefficients in stochastic boundary value problems (SBVP) is addressed, where the data used in the identification correspond to measurements of the displacement field along the boundary of domains subjected to specified external forcing and an inverse problem is formulated to calculate the corresponding, optimal realization of the coefficients of the unknown random field on the adapted basis.
Journal ArticleDOI
An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method
Xiang Ma,Nicholas Zabaras +1 more
TL;DR: In this paper, an adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters.
Journal ArticleDOI
Identification of Bayesian posteriors for coefficients of chaos expansions
TL;DR: It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem and the estimated polynomial chaos coefficients are characterized as random variables whose probability density function is theBayesian posterior.
Journal ArticleDOI
Monte Carlo Solution of Nonlinear Vibrations
Masanobu Shinozuka,Y. K. Wen +1 more
TL;DR: In this article, a Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections, where the pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space.
Journal ArticleDOI
Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data
TL;DR: In this paper, the identification of high-dimensional polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data is studied.
Related Papers (5)
Creating efficient nonlinear neural network process models that allow model interpretation
Gary M. Scott,W. Harmon Ray +1 more
Mathematical Models of Complex Systems on the Basis of Artificial Neural Networks
A. N. Vasilyev,D. A. Tarkhov +1 more
Model order reduction using neural network principal component analysis and generalized dimensional analysis
F. H. Bellamine,Ali Elkamel +1 more