Machine learning and domain decomposition methods-a survey

A Klawonn, M Lanser, J Weber - Computational Science and Engineering, 2024 - Springer
Hybrid algorithms, which combine black-box machine learning methods with experience
from traditional numerical methods and domain expertise from diverse application areas, are …

Enhancing training of physics-informed neural networks using domain decomposition–based preconditioning strategies

A Kopaničáková, H Kothari, GE Karniadakis… - SIAM Journal on …, 2024 - SIAM
We propose to enhance the training of physics-informed neural networks. To this aim, we
introduce nonlinear additive and multiplicative preconditioning strategies for the widely used …

Two-level overlap** additive Schwarz preconditioner for training scientific machine learning applications

Y Lee, A Kopaničáková, GE Karniadakis - ar** additive Schwarz preconditioner for accelerating
the training of scientific machine learning applications. The design of the proposed …

Model Parallel Training and Transfer Learning for Convolutional Neural Networks by Domain Decomposition

A Klawonn, M Lanser, J Weber - arxiv preprint arxiv:2408.14442, 2024 - arxiv.org
Deep convolutional neural networks (CNNs) have been shown to be very successful in a
wide range of image processing applications. However, due to their increasing number of …

Domain-decomposed image classification algorithms using linear discriminant analysis and convolutional neural networks

A Klawonn, M Lanser, J Weber - arxiv preprint arxiv:2410.23359, 2024 - arxiv.org
In many modern computer application problems, the classification of image data plays an
important role. Among many different supervised machine learning models, convolutional …

DDU-Net: A Domain Decomposition-based CNN for High-Resolution Image Segmentation on Multiple GPUs

C Verburg, A Heinlein, EC Cyr - arxiv preprint arxiv:2407.21266, 2024 - arxiv.org
The segmentation of ultra-high resolution images poses challenges such as loss of spatial
information or computational inefficiency. In this work, a novel approach that combines …

Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods

K Trotti, SAC Alegría, A Kopaničáková… - arxiv preprint arxiv …, 2023 - arxiv.org
We propose to train neural networks (NNs) using a novel variant of the``Additively
Preconditioned Trust-region Strategy''(APTS). The proposed method is based on a …

[PDF][PDF] Applied Mathematics and Nonlinear Sciences

Y Wang - Sciences, 2024 - sciendo.com
With the rapid growth of data centers, optimizing energy consumption has become a critical
challenge. This paper proposes an energy management framework that integrates Long …

Unsupervised convolution neural operator preconditioning for the solution of some heterogeneous fluid PDEs

Y **ang - 2025 - inria.hal.science
This work exclusively focuses on using convolution neural operator learning for accelerating
the solution of some heterogenous PDEs (including Poisson equations, Darcy flow …

Research and Implementation of Electricity Meter Wiring Recognition Algorithm based on Machine Learning

Y Fan, B Zhou, Y Jie, K Niu - … of the 2024 International Symposium on …, 2024 - dl.acm.org
In power monitoring and management, accurate acquisition of meter reading is critical for
energy analysis and electricity calculation. However, most of the existing electricity meters …