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

Artificial neural networks (ANNs), which are inspired by the brain, are a central pillar in the ongoing breakthrough in artificial intelligence. In recent years, researchers have examined mechanical implementations of ANNs, denoted as…

In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different…

Kolmogorov-Arnold Networks (KANs) introduce a paradigm of neural modeling that implements learnable functions on the edges of the networks, diverging from the traditional node-centric activations in neural networks. This work assesses the…

Deep neural networks have become a pervasive tool in science and engineering. However, modern deep neural networks' growing energy requirements now increasingly limit their scaling and broader use. We propose a radical alternative for…

Resistance spot welding is the dominant joining process for the body-in-white in the automotive industry, where the weld nugget diameter is the key quality metric. Its measurement requires destructive testing, limiting the potential for…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

The current contribution develops a Variational Physics-Informed Neural Network (VPINN)-based framework for the analysis and design of multiphase architected solids. The elaborated VPINN methodology is based on the Petrov-Galerkin approach,…

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…

Physics-informed Kolmogorov-Arnold Networks (PIKANs), and in particular their Chebyshev-based variants (cPIKANs), have recently emerged as promising models for solving partial differential equations (PDEs). However, their training dynamics…

Multi-layer perceptrons (MLP's) have been extensively utilized in discovering Deep Koopman operators for linearizing nonlinear dynamics. With the emergence of Kolmogorov-Arnold Networks (KANs) as a more efficient and accurate alternative to…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

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…

Hyperspectral image classification is a crucial but challenging task due to the high dimensionality and complex spatial-spectral correlations inherent in hyperspectral data. This paper employs Wavelet-based Kolmogorov-Arnold Network…

Inspired by the Kolmogorov-Arnold superposition theorem, Kolmogorov-Arnold Networks (KANs) have recently emerged as an improved backbone for most deep learning frameworks, promising more adaptivity than their multilayer perceptron (MLP)…

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…

In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth…

Recent advances in aerial robotics have enabled the use of multirotor vehicles for autonomous payload transportation. Resorting only to classical methods to reliably model a quadrotor carrying a cable-slung load poses significant…

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

Physically Guided Neural Networks with Internal Variables are SciML tools that use only observable data for training and and have the capacity to unravel internal state relations. They incorporate physical knowledge both by prescribing the…