Machine learning applied in the multi-scale 3D stress modelling

TL;DR

This paper introduces a hybrid approach combining finite element modeling and neural networks to efficiently estimate multi-scale subsurface stress with high accuracy, reducing computational costs.

Contribution

It presents a novel multi-scale stress modeling methodology that integrates coarse finite element solutions with neural network estimates for fine-scale details.

Findings

Achieves within 2% error compared to high-resolution models

Reduces computational cost of multi-scale stress estimation

Demonstrates applicability through a worked example

Abstract

This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical modeling of systems whose behavior involves a wide span of length scales. One low-frequency solution is obtained via inexpensive finite element modeling at a coarse scale. The second solution provides the fine-grained details introduced by the heterogeneity of the free parameters at the fine scale. This high-frequency solution is estimated via neural networks -trained with partial solutions obtained in high-resolution finite-element models. When the coarse finite element solutions are combined with the neural network estimates, the results are within a 2\% error of the results that would be computed with high-resolution finite element models. This paper discusses the benefits and drawbacks of the method and illustrates their applicability via a worked example.