Related papers: DeepOKAN: Deep Operator Network Based on Kolmogoro…

Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by…

Efficient chemical kinetic model inference and application in combustion are challenging due to large ODE systems and widely separated time scales. Machine learning techniques have been proposed to streamline these models, though strong…

AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that there is…

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer…

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide…

We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the…

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently…

Deep learning has long been dominated by multi-layer perceptrons (MLPs), which have demonstrated superiority over other optimizable models in various domains. Recently, a new alternative to MLPs has emerged - Kolmogorov-Arnold Networks…

We firstly simulated disease dynamics by KAN (Kolmogorov-Arnold Networks) nearly 4 years ago, but the kernel functions in the edge include the exponential number of infected and discharged people and is also in line with the…

Magnetotelluric (MT) forward modeling is fundamental for improving the accuracy and efficiency of MT inversion. Neural operators (NOs) have been effectively used for rapid MT forward modeling, demonstrating their promising performance in…

Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture…

In this paper, we introduce a probabilistic extension to Kolmogorov Arnold Networks (KANs) by incorporating Gaussian Process (GP) as non-linear neurons, which we refer to as GP-KAN. A fully analytical approach to handling the output…

Kolmogorov-Arnold Networks (KANs) were proposed as an alternative to traditional neural network architectures based on multilayer perceptrons (MLP-NNs). The potential advantages of KANs over MLP-NNs, including significantly enhanced…

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…

Medical image enhancement and segmentation are critical yet challenging tasks in modern clinical practice, constrained by artifacts and complex anatomical variations. Traditional deep learning approaches often rely on complex architectures…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

Functional connectivity (FC) analysis, a valuable tool for computer-aided brain disorder diagnosis, traditionally relies on atlas-based parcellation. However, issues relating to selection bias and a lack of regard for subject specificity…

We explore various neural network architectures for modeling the dynamics of the cryptocurrency market. Traditional linear models often fall short in accurately capturing the unique and complex dynamics of this market. In contrast, Deep…

The rapid development of deepfake generation techniques necessitates robust face forgery detection algorithms. While methods based on Convolutional Neural Networks (CNNs) and Transformers are effective, there is still room for improvement…