Prediction of numerical homogenization using deep learning for the Richards equation

Stepanov, Sergei; Spiridonov, Denis; Mai, Tina

doi:10.1016/j.cam.2022.114980

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Fine-grid Discretization and Picard Iteration For Linearization1

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2025

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Cited by 11 publications

(1 citation statement)

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“…For later use, we also define the function space V h = V 3 h . Nonlinear Solve: Inspired by one of the authors' previous works [25,26,51,43,62], we use Picard linearization to deal with nonlinearities. At the beginning of this Picard iterative process, we guess…”

Section: Fine-grid Discretization and Picard Iteration For Linearizationmentioning

confidence: 99%

Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method

Ammosov

Efendiev

Grekova

et al. 2022

Journal of Computational Physics

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Section: Fine-grid Discretization and Picard Iteration For Linearizationmentioning

confidence: 99%

Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method

Ammosov

Efendiev

Grekova

et al. 2022

Journal of Computational Physics

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A review of convolutional neural networks in computer vision

Zhao,

Wang,

Zhang

et al. 2024

Artif Intell Rev

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In computer vision, a series of exemplary advances have been made in several areas involving image classification, semantic segmentation, object detection, and image super-resolution reconstruction with the rapid development of deep convolutional neural network (CNN). The CNN has superior features for autonomous learning and expression, and feature extraction from original input data can be realized by means of training CNN models that match practical applications. Due to the rapid progress in deep learning technology, the structure of CNN is becoming more and more complex and diverse. Consequently, it gradually replaces the traditional machine learning methods. This paper presents an elementary understanding of CNN components and their functions, including input layers, convolution layers, pooling layers, activation functions, batch normalization, dropout, fully connected layers, and output layers. On this basis, this paper gives a comprehensive overview of the past and current research status of the applications of CNN models in computer vision fields, e.g., image classification, object detection, and video prediction. In addition, we summarize the challenges and solutions of the deep CNN, and future research directions are also discussed.

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A computational macroscopic model of piezomagnetoelectric materials using Generalized Multiscale Finite Element Method

Ammosov

Наседкин

Muratova

2024

Journal of Computational and Applied Mathematics

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Prediction of numerical homogenization using deep learning for the Richards equation

Cited by 11 publications

References 65 publications

Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method

Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method

A review of convolutional neural networks in computer vision

A computational macroscopic model of piezomagnetoelectric materials using Generalized Multiscale Finite Element Method

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