Related papers: Physics-Informed Kolmogorov-Arnold Networks for mu…

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the…

Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…

We explore the possibilities of using energy minimization for the numerical modeling of strain localization in solids as a sharp discontinuity in the displacement field. For this purpose, we consider (regularized) strong discontinuity…

The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown…

Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contrast to multilayer perceptrons (MLPs), Kolmogorov-Arnold…

This work introduces Probabilistic Kolmogorov-Arnold Network (P-KAN), a novel probabilistic extension of Kolmogorov-Arnold Networks (KANs) for time series forecasting. By replacing scalar weights with spline-based functional connections and…

Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis…

Friction modeling plays a crucial role in achieving high-precision motion control in robotic operating systems. Traditional static friction models (such as the Stribeck model) are widely used due to their simple forms; however, they…

Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer…

Kolmogorov-Arnold Networks represent a recent advancement in machine learning, with the potential to outperform traditional perceptron-based neural networks across various domains as well as provide more interpretability with the use of…

Kolmogorov-Arnold Networks (KANs) have shown potential as an alternative to Multi-Layer Perceptrons (MLPs) in neural networks, providing universal function approximation with fewer parameters and reduced memory usage. In this paper, we…

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…

The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. This shift is driven by the limitations of MLPs, including poor…

Scientific discovery and dynamic characterization of the physical system play a critical role in understanding, learning, and modeling the physical phenomena and behaviors in various fields. Although theories and laws of many system…

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…

Kolmogorov-Arnold Networks (KANs) offer a theoretically grounded alternative to multi-layer perceptrons by representing multivariate functions as compositions of univariate basis functions. However, a critical limitation of KANs is the need…

Symbolic neural networks, such as Kolmogorov-Arnold Networks (KAN), offer a promising approach for integrating prior knowledge with data-driven methods, making them valuable for addressing inverse problems in scientific and engineering…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from…

The computational cost of geochemical solvers is a challenging matter. For reactive transport simulations, where chemical calculations are performed up to billions of times, it is crucial to reduce the total computational time. Existing…