Related papers: Multilevel CNNs for Parametric PDEs based on Adapt…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…

Deploying deep convolutional neural networks (CNNs) on resource-constrained devices presents significant challenges due to their high computational demands and rigid, static architectures. To overcome these limitations, this thesis explores…

There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3)…

In context of the universal presence of defects in additively manufactured (AM) metals, efficient computational tools are required to rapidly screen AM microstructures for mechanical integrity. To this end, a deep learning approach is used…

The customizable nature of deep learning models have allowed them to be successful predictors in various disciplines. These models are often trained with respect to thousands or millions of instances for complicated problems, but the…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…

The use of Convolutional Neural Networks (CNNs) is widespread in Deep Learning due to a range of desirable model properties which result in an efficient and effective machine learning framework. However, performant CNN architectures must be…

Convolutional Neural Networks (CNNs) have shown strong promise for analyzing scientific data from many domains including particle imaging detectors. However, the challenge of choosing the appropriate network architecture (depth, kernel…

Convolutional Neural Networks (CNNs) have proven to be a powerful state-of-the-art method for image classification tasks. One drawback however is the high computational complexity and high memory consumption of CNNs which makes them…

Convolutional neural networks (CNNs) have shown great capability of solving various artificial intelligence tasks. However, the increasing model size has raised challenges in employing them in resource-limited applications. In this work, we…

We propose a dual pathway, 11-layers deep, three-dimensional Convolutional Neural Network for the challenging task of brain lesion segmentation. The devised architecture is the result of an in-depth analysis of the limitations of current…

Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities. Commonly, the convolution operators couple features from all…

Accurate medical image segmentation is essential for diagnosis and treatment planning of diseases. Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance for automatic medical image segmentation. However, they are…