Related papers: Learning Interface Conditions in Domain Decomposit…
By integrating physics-informed neural network (PINN) techniques with domain decomposition method, a deep domain decomposition method is presented for solving elliptic variational inequality problems. Based on the Ritz variation method, the…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data,…
While the deployment of deep learning models on edge devices is increasing, these models often lack robustness when faced with dynamic changes in sensed data. This can be attributed to sensor drift, or variations in the data compared to…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…
This paper presents GridNet, a new Convolutional Neural Network (CNN) architecture for semantic image segmentation (full scene labelling). Classical neural networks are implemented as one stream from the input to the output with subsampling…
Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics…
Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality…
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
Specifying a complete domain model is time-consuming, which has been a bottleneck of AI planning technique application in many real-world scenarios. Most classical domain-model learning approaches output a domain model in the form of the…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Multi-Activation Function (MAF) approach employs two…
Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…
Deep Learning (DL) models proved themselves to perform extremely well on a wide variety of learning tasks, as they can learn useful patterns from large data sets. However, purely data-driven models might struggle when very difficult…
Graph Neural Networks (GNNs) are prominent in handling sparse and unstructured data efficiently and effectively. Specifically, GNNs were shown to be highly effective for node classification tasks, where labelled information is available for…
Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic…
Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art method for graph-based learning tasks. However, training GCNs at scale is still challenging, hindering both the exploration of more sophisticated GCN architectures and…
Non-local self-similarity is well-known to be an effective prior for the image denoising problem. However, little work has been done to incorporate it in convolutional neural networks, which surpass non-local model-based methods despite…