相关论文: Deep Learning Discrete Calculus (DLDC): A Family o…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…

Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are…

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally…

The feasibility of deep neural networks (DNNs) to address data stream problems still requires intensive study because of the static and offline nature of conventional deep learning approaches. A deep continual learning algorithm, namely…

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

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,…

Deep Learning (DL) has shown great promise in the unsupervised task of clustering. That said, while in classical (i.e., non-deep) clustering the benefits of the nonparametric approach are well known, most deep-clustering methods are…

The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within…

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…

Multi-label learning is a rapidly growing research area that aims to predict multiple labels from a single input data point. In the era of big data, tasks involving multi-label classification (MLC) or ranking present significant and…

Deep learning (DL) is one of the fastest growing topics in materials data science, with rapidly emerging applications spanning atomistic, image-based, spectral, and textual data modalities. DL allows analysis of unstructured data and…

Context: Automated software defect prediction (SDP) methods are increasingly applied, often with the use of machine learning (ML) techniques. Yet, the existing ML-based approaches require manually extracted features, which are cumbersome,…

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…

Multiple clustering has gathered significant attention in recent years due to its potential to reveal multiple hidden structures of the data from different perspectives. Most of multiple clustering methods first derive feature…

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…

Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference…

Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…