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We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset…

Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Hyperspectral image classification is a crucial but challenging task due to the high dimensionality and complex spatial-spectral correlations inherent in hyperspectral data. This paper employs Wavelet-based Kolmogorov-Arnold Network…

Superpixels have been widely used in computer vision tasks due to their representational and computational efficiency. Meanwhile, deep learning and end-to-end framework have made great progress in various fields including computer vision.…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Inspired by the Kolmogorov-Arnold superposition theorem, Kolmogorov-Arnold Networks (KANs) have recently emerged as an improved backbone for most deep learning frameworks, promising more adaptivity than their multilayer perceptron (MLP)…

Continual learning requires models to train continuously across consecutive tasks without forgetting. Most existing methods utilize linear classifiers, which struggle to maintain a stable classification space while learning new tasks.…

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…

Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However,…

Kolmogorov-Arnold Networks (KAN) has recently attracted significant attention as a promising alternative to traditional Multi-Layer Perceptrons (MLP). Despite their theoretical appeal, KAN require validation on large-scale benchmark…

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth…

Solving partial differential equations (PDEs) is essential in scientific forecasting and fluid dynamics. Traditional approaches often incur expensive computational costs and trade-offs in efficiency and accuracy. Recent deep neural networks…

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets…

While accurate, black-box system identification models lack interpretability of the underlying system dynamics. This paper proposes State-Space Kolmogorov-Arnold Networks (SS-KAN) to address this challenge by integrating Kolmogorov-Arnold…

In the realm of intelligent education, cognitive diagnosis plays a crucial role in subsequent recommendation tasks attributed to the revealed students' proficiency in knowledge concepts. Although neural network-based neural cognitive…

Many Partial Differential Equations (PDEs) do not have analytical solution, and can only be solved by numerical methods. In this context, Physics-Informed Neural Networks (PINN) have become important in the last decades, since it uses a…

With increasing penetration of distributed energy resources installed behind the meter, there is a growing need for adequate modelling of composite loads to enable accurate power system simulation analysis. Existing measurement based load…

Kolmogorov-Arnold Network (KAN) is a network structure recently proposed by Liu et al. (2024) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work…

We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…