Related papers: Geometric Kolmogorov--Arnold Network (GeoKAN)

Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold…

Kolmogorov-Arnold Networks (KANs) offer a structured and interpretable framework for multivariate function approximation by composing univariate transformations through additive or multiplicative aggregation. This paper establishes…

Kolmogorov Arnold Networks (KANs) are recent architectural advancement in neural computation that offer a mathematically grounded alternative to standard neural networks. This study presents an empirical evaluation of KANs in context of…

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to…

This paper presents the development and application of Wavelet Kolmogorov-Arnold Networks (Wav-KAN) in federated learning. We implemented Wav-KAN \cite{wav-kan} in the clients. Indeed, we have considered both continuous wavelet transform…

The application of machine learning methodologies for predicting properties within materials science has garnered significant attention. Among recent advancements, Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to…

Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal Interpolation KAN (FI-KAN), which incorporates learnable…

Gene regulation is central to understanding cellular processes and development, potentially leading to the discovery of new treatments for diseases and personalized medicine. Inferring gene regulatory networks (GRNs) from single-cell RNA…

This paper presents a comprehensive survey of 18 distinct polynomials and their potential applications in Kolmogorov-Arnold Network (KAN) models as an alternative to traditional spline-based methods. The polynomials are classified into…

Graph contrastive learning (GCL) has demonstrated great promise for learning generalizable graph representations from unlabeled data. However, conventional GCL approaches face two critical limitations: (1) the restricted expressive capacity…

Hybrid constitutive modeling integrates two complementary approaches for describing and predicting a material's mechanical behavior: purely data-driven black-box methods and physically constrained, theory-based models. While black-box…

In this paper, we present a novel localized Generative Adversarial Net (GAN) to learn on the manifold of real data. Compared with the classic GAN that {\em globally} parameterizes a manifold, the Localized GAN (LGAN) uses local coordinate…

Content and image generation consist in creating or generating data from noisy information by extracting specific features such as texture, edges, and other thin image structures. We are interested here in generative models, and two main…

Urban traffic optimization is critical for improving transportation efficiency and alleviating congestion, particularly in large-scale dynamic networks. Traditional methods, such as Dijkstra's and Floyd's algorithms, provide effective…

Data science has emerged as fourth paradigm of scientific exploration. However many machine learning models operate as black boxes offering limited insight into the reasoning behind their predictions. This lack of transparency is one of the…

Kolmogorov-Arnold Networks (KANs) have garnered attention for replacing fixed activation functions with learnable univariate functions, but they exhibit practical limitations, including high computational costs and performance deficits in…

The Kolmogorov-Arnold Network (KAN) has recently gained attention as an alternative to traditional multi-layer perceptrons (MLPs), offering improved accuracy and interpretability by employing learnable activation functions on edges. In this…

Kolmogorov-Arnold Networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be…