相关论文: AC-PKAN: Attention-Enhanced and Chebyshev Polynomi…

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…

Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the…

Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently…

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-layer Perceptrons (MLPs) due to their superior function-fitting abilities in data-driven modeling. In this paper, we propose a novel framework, DAE-KAN, for…

Kolmogorov-Arnold Networks (KANs) represent an innovation in neural network architectures, offering a compelling alternative to Multi-Layer Perceptrons (MLPs) in models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks…

We introduce cumulative polynomial Kolmogorov-Arnold networks (CP-KAN), a neural architecture combining Chebyshev polynomial basis functions and quadratic unconstrained binary optimization (QUBO). Our primary contribution involves…

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture,…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful mesh-free framework for solving ordinary and partial differential equations by embedding the governing physical laws directly into the loss function. However, their…

We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep…

Kolmogorov-Arnold Networks (KANs) relocate learnable nonlinearities from nodes to edges, demonstrating remarkable capabilities in scientific machine learning and interpretable modeling. However, current KAN implementations suffer from…

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…

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional…

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential…

Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as…

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs…

Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning models (PIKANs) and deep operator models (DeepOKANs) for solving…

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have…

Physics-informed neural networks have proven to be a powerful tool for solving differential equations, leveraging the principles of physics to inform the learning process. However, traditional deep neural networks often face challenges in…

Kolmogorov-Arnold Networks (KANs) have recently emerged as a compelling alternative to multilayer perceptrons, offering enhanced interpretability via functional decomposition. However, existing KAN architectures, including spline-,…

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…