Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

Wu, Ling; Zulueta, Kepa; Major, Zoltán; Arriaga, Aitor; Noels, Ludovic

doi:10.1016/j.cma.2019.112693

Cited by 47 publications

(29 citation statements)

References 26 publications

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“…In another context in which a feed-forward NNW was trained to predict monotonic response for different material parameters, random combinations of the input variables were used to create the training data in [25]; in this work, 500 random combinations of 6 material parameters were used for the NNW training. Compared to using the input values defined from a regular grids of high dimension data space, the random combination of input variables turned out to be more efficient.…”

Section: Random Loading Pathmentioning

confidence: 99%

“…In finite element simulations, NNWs were used as surrogate for constitutive laws of non-linear materials in [20][21][22], and of rate-dependent materials in [23]. NNWs served as a surrogate for an elasto-plastic material model for parameters identification in [24] and for micro-mechanics model parameters identification in [25]. In this last reference, NNWs were adopted to substitute complex material homogenization constitutive laws to accelerate the massive computations involved in Bayesian inference.…”

Section: Introductionmentioning

confidence: 99%

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A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

Nguyễn

Kilingar

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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143

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An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyzes in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allows generating data for a wide range of strain-stress states and state evolution. The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE 2 multiscale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.

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Section: Random Loading Pathmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

Nguyễn

Kilingar

et al. 2020

Computer Methods in Applied Mechanics and Engineering

Self Cite

143

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“…One of the many applications of Bayes' theorem is Bayesian inference, which is a statistical analysis approach (Wu et al [36]). In Bayesian inference, Bayes' theorem is used to deduce and update properties of an underlying probability distribution with more evidence and information available by computing the posterior probability, which can be expressed by prior probability distribution and the likelihood function.…”

Section: Bayesian Inferencementioning

confidence: 99%

Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model

Ding

Dong

Yang

et al. 2021

Advances in Materials Science and Engineering

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With the increase of the long-span bridge, the damage of the long-span bridge hanger has attracted more and more attention. Nowadays, the probability statistics method based on Bayes’ theorem is widely used for evaluating the damage of bridge, that is, Bayesian inference. In this study, the damage evaluation model of bridge hanger is established based on Bayesian inference. For the damage evaluation model, the analytical expressions for calculating the weights by finite mixture (FM) method are derived. In order to solve the complex analytical expressions in damage evaluation model, the Metropolis-Hastings (MH) sampling of Markov chain Monte Carlo (MCMC) method was used. Three case studies are adopted to demonstrate the effect of the initial value and the applicability of the proposed model. The result suggests that the proposed model can evaluate the damage of the bridge hanger.

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“…Another idea, initiated in [ 27 , 28 ], is the use of so-called data-driven approaches in which microscale calculations are performed offline, and are then used as data in an online stage to reconstruct the macroscopic (effective) behavior. For this purpose, several techniques were proposed, including interpolation methods [ 27 , 29 ], neural networks [ 28 , 30 , 31 , 32 , 33 , 34 , 35 ], Bayesian inference [ 36 ], Fourier series expansions [ 37 ], or Gaussian process regression [ 38 ]. In the related techniques, offline data collection is used in a regression process to construct an accurate surrogate model whose evaluation is several orders of magnitude lower than that performing one RVE nonlinear calculation.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling

Yvonnet

Papadopoulos

et al. 2021

Materials

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A stochastic data-driven multilevel finite-element (FE2) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data. Then, a FE2 method replacing the nonlinear multiscale calculations by the NN–I is developed. The NN–I scheme improved the accuracy of the neural-network surrogate model when insufficient data were available. Due to the achieved reduction in computational time, which was several orders of magnitude less than that to direct FE2, the use of such a machine-learning method is demonstrated for performing Monte Carlo simulations in nonlinear heterogeneous structures and propagating uncertainties in this context, and the identification of probabilistic models at the macroscale on some quantities of interest. Applications to nonlinear electric conduction in graphene–polymer composites are presented.

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Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

Cited by 47 publications

References 26 publications

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model

A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling

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