Related papers: Adaptive neural domain refinement for solving time…
We present a subspace method based on neural networks for solving the partial differential equation in weak form with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
In medical imaging, the heterogeneity of multi-centre data impedes the applicability of deep learning-based methods and results in significant performance degradation when applying models in an unseen data domain, e.g. a new centreor a new…
A practical shortcoming of deep neural networks is their specialization to a single task and domain. While recent techniques in domain adaptation and multi-domain learning enable the learning of more domain-agnostic features, their success…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
Getting deep convolutional neural networks to perform well requires a large amount of training data. When the available labelled data is small, it is often beneficial to use transfer learning to leverage a related larger dataset (source) in…
Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
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…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
We propose associative domain adaptation, a novel technique for end-to-end domain adaptation with neural networks, the task of inferring class labels for an unlabeled target domain based on the statistical properties of a labeled source…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
The lack of out-of-domain generalization is a critical weakness of deep networks for semantic segmentation. Previous studies relied on the assumption of a static model, i. e., once the training process is complete, model parameters remain…
Although deep neural networks have achieved remarkable results for the task of semantic segmentation, they usually fail to generalize towards new domains, especially when performing synthetic-to-real adaptation. Such domain shift is…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…
Deep convolutional neural networks (CNNs) have shown excellent performance in object recognition tasks and dense classification problems such as semantic segmentation. However, training deep neural networks on large and sparse datasets is…