Related papers: Tensor Neural Network Based Machine Learning Metho…

Machine-learning interatomic potentials (MLIPs) have made a significant contribution to the recent progress in the fields of computational materials and chemistry due to the MLIPs' ability of accurately approximating energy landscapes of…

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that…

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…

Image superresolution methods process an input image sequence of a scene to obtain a still image with increased resolution. Classical approaches to this problem involve complex iterative minimization procedures, typically with high…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea…

The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-tensor computational regions. First, we extend the existing…

To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In…

In this work we introduce a new multiscale artificial neural network based on the structure of $\mathcal{H}$-matrices. This network generalizes the latter to the nonlinear case by introducing a local deep neural network at each spatial…

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

This paper proposes a machine-learning-based solution approach for solving multi-horizon stochastic programs. The approach embeds a deep learning neural network into a multi-horizon stochastic program to approximate the recourse operational…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…