相关论文: Simplex-FEM Networks (SiFEN): Learning A Triangula…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Learning representations of nodes has been a crucial area of the graph machine learning research area. A well-defined node embedding model should reflect both node features and the graph structure in the final embedding. In the case of…

This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…

In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…

Single image super-resolution(SISR) has witnessed great progress as convolutional neural network(CNN) gets deeper and wider. However, enormous parameters hinder its application to real world problems. In this letter, We propose a…

Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Background: Federated Learning (FL) has emerged as a promising paradigm for training machine learning models while preserving data privacy. However, applying FL to Natural Language Processing (NLP) tasks presents unique challenges due to…

We present a novel formulation for modeling phase-field fracture propagation based on the Integrated Finite Element Neural Network (IFENN) framework. IFENN is a hybrid solver scheme that utilizes neural networks as PDE solvers within FEM,…

In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same…

We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with Stiefel-constrained parameters. Unlike standard Euclidean averaging, which violates orthogonality,…

We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator…

We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via common faces and cofaces independently…

We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Networks (EFENN) introduced with the Hierarchical Deep-learning…

This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

Deep learning, a rebranding of deep neural network research works, has achieved a remarkable success in recent years. With multiple hidden layers, deep learning models aim at computing the hierarchical feature representations of the…

Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral…

In deep learning models, learning more with less data is becoming more important. This paper explores how neural networks with normalized Radial Basis Function (RBF) kernels can be trained to achieve better sample efficiency. Moreover, we…