相关论文: Adaptive Multi-Grade Deep Learning for Highly Osci…

We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the equation exhibits certain oscillatory behaviors due to the…

The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs). Deep neural networks (DNNs) have received super performance in solving PDEs in addition to their outstanding success in…

Multi-grade deep learning (MGDL) has been shown to significantly outperform the standard single-grade deep learning (SGDL) across various applications. This work aims to investigate the computational advantages of MGDL focusing on its…

We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures…

Deep neural networks (DNNs) suffer from the spectral bias, wherein DNNs typically exhibit a tendency to prioritize the learning of lower-frequency components of a function, struggling to capture its high-frequency features. This paper is to…

This paper introduces a successive affine learning (SAL) model for constructing deep neural networks (DNNs). Traditionally, a DNN is built by solving a non-convex optimization problem. It is often challenging to solve such a problem…

Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs): deep neural networks (DNNs) architectures motivated by fixed-point iteration schemes for the solution of linear and nonlinear Fredholm…

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering…

Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…

Meta-learning that uses implicit gradient have provided an exciting alternative to standard techniques which depend on the trajectory of the inner loop training. Implicit meta-learning (IML), however, require computing $2^{nd}$ order…

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,…

In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…

The exponential growth in the number of complex datasets every year requires more enhancement in machine learning methods to provide robust and accurate data classification. Lately, deep learning approaches have achieved surpassing results…

We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of…

Recent state-of-the-art active learning methods have mostly leveraged Generative Adversarial Networks (GAN) for sample acquisition; however, GAN is usually known to suffer from instability and sensitivity to hyper-parameters. In contrast to…

Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…

Stochastic volatility models, where the volatility is a stochastic process, can capture most of the essential stylized facts of implied volatility surfaces and give more realistic dynamics of the volatility smile/skew. However, they come…

The continually increasing number of complex datasets each year necessitates ever improving machine learning methods for robust and accurate categorization of these data. This paper introduces Random Multimodel Deep Learning (RMDL): a new…

The whole slide histopathology images (WSIs) play a critical role in gastric cancer diagnosis. However, due to the large scale of WSIs and various sizes of the abnormal area, how to select informative regions and analyze them are quite…