Related papers: Data-driven discoveries of B\"acklund transforms a…

We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture…

Spectral-spatial based deep learning models have recently proven to be effective in hyperspectral image (HSI) classification for various earth monitoring applications such as land cover classification and agricultural monitoring. However,…

Recent work on deep learning for tabular data demonstrates the strong performance of deep tabular models, often bridging the gap between gradient boosted decision trees and neural networks. Accuracy aside, a major advantage of neural models…

Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the…

Artificial intelligence systems, particularly through generative pre-trained transformers (GPTs), have enabled capability-rich language models, but their operation incurs substantial costs in digital computation, memory, and data movement.…

We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of…

Complex spin-spin interactions in magnets can often lead to magnetic superlattices with complex local magnetic arrangements, and many of the magnetic superlattices have been found to possess non-trivial topological electronic properties.…

Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems.…

The implementation of deep learning algorithms has brought new perspectives to plankton ecology. Emerging as an alternative approach to established methods, deep learning offers objective schemes to investigate plankton organisms in diverse…

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for…

Online deep learning tackles the challenge of learning from data streams by balancing two competing goals: fast learning and deep learning. However, existing research primarily emphasizes deep learning solutions, which are more adept at…

The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on $R^{2,2}$. It has a Lax pair and is an integrable system. Ward constructed…

This paper investigates data-driven solutions and parameter discovery to (2+1)-dimensional coupled nonlinear Schr\"odinger equations with variable coefficients (VC-CNLSEs), which describe transverse effects in optical fiber systems under…

Data transformations (e.g. rotations, reflections, and cropping) play an important role in self-supervised learning. Typically, images are transformed into different views, and neural networks trained on tasks involving these views produce…

There is growing interest in neural network architectures for tabular data. Many general-purpose tabular deep learning models have been introduced recently, with performance sometimes rivaling gradient boosted decision trees (GBDTs). These…

Deep neural networks (DNN) have been used successfully in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. In this paper, we…

Deep Neural Networks (DNNs) have been successfully applied to a wide range of problems. However, two main limitations are commonly pointed out. The first one is that they require long time to design. The other is that they heavily rely on…

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…

This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different…

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…