Predicting the Non-Deterministic Response of a Micro-Scale Mechanical Model Using Generative Adversarial Networks

Abstract

Recent improvements in micro-scale material descriptions allow to build increasingly refined multiscale models in geomechanics. This often comes at the expense of computational cost which can eventually become prohibitive. Among other characteristics, the non-determinism of a micro-scale response makes its replacement by a surrogate particularly challenging. Machine Learning (ML) is a promising technique to substitute physics-based models, nevertheless existing ML algorithms for the prediction of material response do not integrate non-determinism in the learning process. Is it possible to use the numerical output of the latest micro-scale descriptions to train a ML algorithm that will then provide a response at a much lower computational cost? A series of ML algorithms with different levels of depth and supervision are trained using a data-driven approach. Gaussian Process Regression (GPR), Self-Organizing Maps (SOM) and Generative Adversarial Networks (GANs) are tested and the latter retained because of its superior results. A modified GANs with lower network depth showed good performance in the generation of failure probability maps, with good reproduction of the non-deterministic micro-scale response. The trained generator can be incorporated into existing multiscale models allowing to, at least partially, bypass the costly micro-scale computations.

FEM-GAN: A Physics-Supervised Deep Learning Generative Model for Elastic Porous Materials

“…Numerous GAN variants have been proposed since its initial introduction in 2017, including Least Squares Generative Adversarial Networks (LSGANs) by Mao et al [ 43 ] and Wasserstein Generative Adversarial Networks (WGANs) by Arjovsky et al [ 44 ], among others, and they play an essential role in the generation of artificial images, audio signals, and others. GANs can be used as generative models [ 45 ] and as predictive models as well [ 46 , 47 ].…”

Improved particle swarm optimizer for problems with variable evaluation time: Application to asymptotic homogenization

“…The optimization domain is bounded for the three input parameters with values: $$$$ {\displaystyle \begin{array}{cc}\hfill {\Delta}_n\in \left[0.002,0.012\right]\kern0.3em \mathrm{mm},& \\ {}\hfill \mu \in \left[0.5\times 1{0}^9,5.0\times 1{0}^9\right]\kern0.3em \mathrm{Pa},& \hfill \\ {}\hfill G\in \left[0.7\times 1{0}^{13},2.7\times 1{0}^{13}\right]\kern0.3em \mathrm{Pa},& \end{array}} $$$$ and using the reference values $$$ \left[{\Delta}_{n, ref},{\mu}_{ref},{G}_{ref}\right]=\left[0.0050\kern0.3em \mathrm{mm},\kern0.3em 9.61\times 1{0}^8\kern0.3em \mathrm{Pa},\kern0.3em 2.00\times 1{0}^{13}\kern0.3em \mathrm{Pa}\right] $$$. The non‐convexity of the failure surface together with the non‐unicity of the response 64 are the reasons why metaheuristics are suitable for the present application.…”

“…Swarm size 40 . The non-convexity of the failure surface together with the non-unicity of the response 64 are the reasons why metaheuristics are suitable for the present application.…”