arXiv subjects

Michalis Papachristou

Publications and source records attributed to Michalis Papachristou.

5 recordsLinked to original sources

arXiv2025

Training Deep Physics-Informed Kolmogorov-Arnold Networks

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, Chebyshev-based physics-informed KANs (cPIKANs) have become the standard due to their computational efficiency. However, like their multilayer perceptron-based counterparts, cPIKANs face significant challenges when scaled to depth, leading to training instabilities that limit their applicability to several PDE problems. To address this, we propose a basis-agnostic, Glorot-like initialization scheme that preserves activation variance and yields substantial improvements in stability and accuracy over the default initialization of cPIKANs. Inspired by the PirateNet architecture, we further introduce Residual-Gated Adaptive KANs (RGA KANs), designed to mitigate divergence in deep cPIKANs where initialization alone is not sufficient. Through empirical tests and information bottleneck analysis, we show that RGA KANs successfully traverse all training phases, unlike baseline cPIKANs, which stagnate in the diffusion phase in specific PDE settings. Evaluations on nine standard forward PDE benchmarks under a fixed training pipeline with adaptive components demonstrate that RGA KANs consistently outperform parameter-matched cPIKANs and PirateNets - often by several orders of magnitude - while remaining stable in settings where the others diverge.

cs.LG↗

arXiv2025

Explainable fault and severity classification for rolling element bearings using Kolmogorov-Arnold networks

Rolling element bearings are critical components of rotating machinery, with their performance directly influencing the efficiency and reliability of industrial systems. At the same time, bearing faults are a leading cause of machinery failures, often resulting in costly downtime, reduced productivity, and, in extreme cases, catastrophic damage. This study presents a methodology that utilizes Kolmogorov-Arnold Networks to address these challenges through automatic feature selection, hyperparameter tuning and interpretable fault analysis within a unified framework. By training shallow network architectures and minimizing the number of selected features, the framework produces lightweight models that deliver explainable results through feature attribution and symbolic representations of their activation functions. Validated on two widely recognized datasets for bearing fault diagnosis, the framework achieved perfect F1-Scores for fault detection and high performance in fault and severity classification tasks, including 100% F1-Scores in most cases. Notably, it demonstrated adaptability by handling diverse fault types, such as imbalance and misalignment, within the same dataset. The symbolic representations enhanced model interpretability, while feature attribution offered insights into the optimal feature types or signals for each studied task. These results highlight the framework's potential for practical applications, such as real-time machinery monitoring, and for scientific research requiring efficient and explainable models.

cs.LG↗

arXiv2024

Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks

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. Traditionally, Multilayer Perceptrons (MLPs) have been the neural network of choice, with significant progress made in optimizing their training. Recently, Kolmogorov-Arnold Networks (KANs) were introduced as a viable alternative, with the potential of offering better interpretability and efficiency while requiring fewer parameters. In this paper, we present a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving PDEs, achieving up to 84 times faster training times than the original KAN implementation. We propose an adaptive training scheme for PIKANs, introducing an adaptive state transition technique to avoid loss function peaks between grid extensions, and a methodology for designing PIKANs with alternative basis functions. Through comparative experiments, we demonstrate that the adaptive features significantly enhance solution accuracy, decreasing the L^2 error relative to the reference solution by up to 43.02%. For the studied PDEs, our methodology approaches or surpasses the results obtained from architectures that utilize up to 8.5 times more parameters, highlighting the potential of adaptive, grid-dependent PIKANs as a superior alternative in scientific and engineering applications.

cs.LG↗

arXiv2023

A plausible link between dynamically unsettled molecular gas and the radio jet in NGC 6328

We report the detection of outflowing molecular gas at the center of the nearby radio galaxy NGC6328 (z=0.014), which has a gigahertz-peaked spectrum radio core and a compact (2 pc) young double radio lobe tracing jet. Utilizing Atacama Large Millimeter/submillimeter Array (ALMA) CO(2-1) and CO(3-2) observations, as well as a novel code developed to fit the 3D gas distribution and kinematics, to study the molecular gas kinematics, we find that the bulk of the gas is situated within a highly warped disk structure, most likely the result of a past merger event. Our analysis further uncovers, within the inner regions of the gas distribution (R<300 pc) and at a position angle aligning with that of the radio jet (150 degrees), the existence of two anti-diametric molecular gas structures kinematically detached from the main disk. These structures most likely trace a jet-induced cold gas outflow with a total lower limit mass of $2\times 10^6\,\mathrm{M_\odot}$ mass, corresponding to an outflow rate of $2\,\mathrm{M_\odot\,yr^{-1}}$ and a kinetic power of $2.7\times 10^{40}\,\mathrm{erg\,s^{-1}}$. The energy required to maintain such a molecular outflow is aligned with the mechanical power of the jet.

astro-ph.GA↗

arXiv2021

CO kinematics unveil outflows plausibly driven by a young jet in the Gigahertz Peaked Radio Core of NGC6328

We report the detection of outflowing molecular gas in the center of the nearby (z=0.014) massive radio galaxy NGC6328. The radio core of the galaxy, PKS B1718-649, is identified as a Gigahertz Peaked Spectrum source with a compact (2 pc) double radio lobe morphology. We used ALMA CO(2-1) and CO(3-2) observations at 100 pc resolution to study the gas kinematics up to ~5 kpc from the galaxy center. While the bulk of the molecular gas is settled in a highly warped disk, in the inner 300 pc of the disk and along with the orientation of the radio jet, we identified high-excitation and high-velocity gas that cannot be attributed to any regular kinematic component based on our detailed 3D modeling of the ALMA data. The high-velocity dispersion in the gas also suggests that it is not part of an inflowing, shredding structure. These results suggest the presence of a molecular outflow of 3 to 8 solar masses per year. The outflow possibly originated from the interaction of the jet with the dense interstellar medium, even though the radio emission is detected closer to the center than the outflow. In this sense, this source resembles NGC1377, 4C31.04 and ESO420-G13, in which the outflows are linked to faint or past jet activity.

astro-ph.GA↗