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Updated: Nov 3, 2025

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling
Xiaoxin Lu1, Julien Yvonnet2, Leonidas Papadopoulos3
1Shenzhen Institute of advanced electronic materials, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518103, China.
Abstract:
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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