相关论文: Tailored Finite Point Operator Networks for Interf…

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing…

Autonomous driving is the key technology of intelligent logistics in Industrial Internet of Things (IIoT). In autonomous driving, the appearance of incomplete point clouds losing geometric and semantic information is inevitable owing to…

Although FFT-based methods are renowned for their numerical efficiency and stability, traditional discretizations fail to capture material interfaces that are not aligned with the grid, resulting in suboptimal accuracy. To address this…

Recurrent neural networks are widely used in speech and language processing. Due to dependency on the past, standard algorithms for training these models, such as back-propagation through time (BPTT), cannot be efficiently parallelised.…

In this paper, we propose a new general and stable fixed-point approach to compute the resolvents of the composition of a set-valued maximal monotone operator with a linear bounded mapping. Weak, strong and linear convergence of the…

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…

Personalized Federated Learning (PFL) has witnessed remarkable advancements, enabling the development of innovative machine learning applications that preserve the privacy of training data. However, existing theoretical research in this…

Phase-field models have been widely used to investigate the phase transformation phenomena. However, it is difficult to solve the problems numerically due to their strong nonlinearities and higher-order terms. This work is devoted to…

We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…

This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…

We present an approach to matching images of objects in fine-grained datasets without using part annotations, with an application to the challenging problem of weakly supervised single-view reconstruction. This is in contrast to prior works…

We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…

In this work, we present Point Transformer, a deep neural network that operates directly on unordered and unstructured point sets. We design Point Transformer to extract local and global features and relate both representations by…

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…