Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media

2018/10/03 by Maria Vasilyeva, Vasilyeva, Maria, Aleksey Tyrylgin +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1810.01586

openalex publication_date 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we consider a numerical homogenization of the poroelasticity problem with stochastic properties. The proposed method based on the construction of the deep neural network (DNN) for fast calculation of the effective properties for a coarse grid approximation of the problem. We train neural networks on the set of the selected realizations of the local microscale stochastic fields and macroscale characteristics (permeability and elasticity tensors). We construct a deep learning method through convolutional neural network (CNN) to learn a map between stochastic fields and effective properties. Numerical results are presented for two and three-dimensional model problems and show that proposed method provide fast and accurate effective property predictions.

Related

• Deep operator network for surrogate modeling of poroelasticity with random permeability fields
• Physics-informed deep learning for flow and deformation in poroelastic media
• Predicting Effective Diffusivity of Porous Media from Images by Deep Learning
• Neural Networks for Predicting Permeability Tensors of 2D Porous Media: Comparison of Convolution- and Transformer-based Architectures
• Deep Convolutional Neural Networks Predict Elasticity Tensors and their Bounds in Homogenization