Related papers: Multi-Resolution Training-Enhanced Kolmogorov-Arno…

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…

Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function.…

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,…

PINNs enhance scientific computing by incorporating physical laws into neural network structures, leading to significant advancements in scientific computing. However, PINNs struggle with multi-scale and high-frequency problems due to…

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…

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…

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…

In continuum topology optimization (TO), two essential procedures are involved: structural analysis through the solution of partial differential equations (PDEs) and the subsequent update of design variables. Both procedures can be…

Since their introduction, Kolmogorov-Arnold Networks (KANs) have been successfully applied across several domains, with physics-informed machine learning (PIML) emerging as one of the areas where they have thrived. In the PIML setting,…

Physics-Informed Neural Networks (PINNs) and more recently Physics-Informed Kolmogorov-Arnold Networks (PIKANs) have emerged as promising approaches for solving partial differential equations (PDEs) without reliance on extensive labeled…

This paper presents, for the first time, a framework for Kolmogorov-Arnold Networks (KANs) in power system applications. Inspired by the recently proposed KAN architecture, this paper proposes physics-informed Kolmogorov-Arnold Networks…

Unmanned aerial vehicle (UAV) communications demand accurate yet interpretable air-to-ground (A2G) channel models that can adapt to nonstationary propagation environments. While deterministic models offer interpretability and deep learning…

Physics-Informed Kolmogorov-Arnold Networks (PIKANs) are gaining attention as an effective counterpart to the original multilayer perceptron-based Physics-Informed Neural Networks (PINNs). Both representation models can address inverse…

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…

Deep Reinforcement Learning (DRL), a subset of machine learning focused on sequential decision-making, has emerged as a powerful approach for tackling financial trading problems. In finance, DRL is commonly used either to generate discrete…

Pansharpening aims to fuse high-resolution spatial details from panchromatic images with the rich spectral information of multispectral images. Existing deep neural networks for this task typically rely on static activation functions, which…

Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid…

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…

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…

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…