Search

In traditional neural network architectures, a multilayer perceptron (MLP) is typically employed as a classification block following the feature extraction stage. However, the Kolmogorov-Arnold Network (KAN) presents a promising alternative to MLP, offering the potential to enhance prediction accuracy. In this paper, we propose the replacement of linear and convolutional layers of traditional networks with KAN-based counterparts. These modifications allowed us to significantly increase the per-pixel classification accuracy for hyperspectral remote-sensing images. We modified seven different neural network architectures for hyperspectral image classification and observed a substantial improvement in the classification accuracy across all the networks. The architectures considered in the paper include baseline MLP, state-of-the-art 1D (1DCNN) and 3D convolutional (two different 3DCNN, NM3DCNN), and transformer (SSFTT) architectures, as well as newly proposed M1DCNN. The greatest effect was achieved for convolutional networks working exclusively on spectral data, and the best classification quality was achieved using a KAN-based transformer architecture. All the experiments were conducted using seven openly available hyperspectral datasets. Our code is available at https://github.com/f-neumann77/HyperKAN.

In this study, we present the original method for reconstructing the potential of interparticle interaction from statistically averaged structural data, namely, the radial distribution function of particles in many-particle system. This method belongs to a family of machine learning methods and is implemented through the differential evolution algorithm. As demonstrated for the case of the Lennard-Jones liquid taken as an example, there is no one-to-one correspondence between structure and potential of interparticle interaction of a many-particle disordered system at a certain thermodynamic state. Namely, a whole family of the Mie potentials determined by two parameters $p_{ 1 }$ and $p_{ 2 }$ related to each other according to a certain rule can reproduce properly a unique structure of the Lennard-Jones liquid at a given thermodynamic state. It is noteworthy that this family of the potentials quite correctly reproduces for the Lennard-Jones liquid the transport properties (in particular, the self-diffusion coefficient) over a temperature range as well as the dynamic structure factor, which is one of the key characteristics of the collective dynamics of particles., Comment: 29 pages, 7 figures