相关论文: Learning Adaptive Constraints in Nonlinear FETI-DP…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

Foundation models (FMs) have shown prominent success in a wide range of tasks. Their applicability to specific domain-task pairings relies on the availability of, both, high-quality data and significant computational resources. These…

Federated Learning (FL) has emerged as a prominent distributed machine learning framework that enables geographically discrete clients to train a global model collaboratively while preserving their privacy-sensitive data. However, due to…

Federated learning (FL) is an effective and widely used approach to training deep learning models on decentralized datasets held by distinct clients. FL also strengthens both security and privacy protections for training data. Common…

Physics-informed machine learning frameworks such as Physics-Informed Neural Networks (PINNs) and Physics-Informed Extreme Learning Machines (PI-ELMs) have shown great promise for solving partial differential equations (PDEs) but struggle…

Federated learning (FL) enables collaboratively training a model while keeping the training data decentralized and private. However, one significant impediment to training a model using FL, especially large models, is the resource…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

As a promising distributed machine learning paradigm, Federated Learning (FL) enables all the involved devices to train a global model collaboratively without exposing their local data privacy. However, for non-IID scenarios, the…

We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

This paper introduces Dynamic Embeddings with Task-Oriented prompting (DETOT), a novel approach aimed at improving the adaptability and efficiency of machine learning models by implementing a flexible embedding layer. Unlike traditional…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

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…

We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…

Federated Learning (FL) enables distributed clients to collaboratively train models without exposing their private data. However, it is difficult to implement efficient FL due to limited resources. Most existing works compress the…

Federated learning (FL) scenarios inherently generate a large communication overhead by frequently transmitting neural network updates between clients and server. To minimize the communication cost, introducing sparsity in conjunction with…

We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…

This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…