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 L2 error relative to the reference solution by up to 43.02%. For the studied forward PDE problems, 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.

The Industrial Internet of Things has enabled the integration and analysis of vast volumes of data across various industries, with the maritime sector being no exception. Advances in cloud computing and deep learning (DL) are continuously reshaping the industry, particularly in optimizing maritime operations such as Predictive Maintenance (PdM). In this study, we propose a novel DL-based framework focusing on the fault detection task of PdM in marine operations, leveraging time-series data from sensors installed on shipboard machinery. The framework is designed as a scalable and cost-efficient software solution, encompassing all stages from data collection and pre-processing at the edge to the deployment and lifecycle management of DL models. The proposed DL architecture utilizes Graph Attention Networks (GATs) to extract spatio-temporal information from the time-series data and provides explainable predictions through a feature-wise scoring mechanism. Additionally, a custom evaluation metric with real-world applicability is employed, prioritizing both prediction accuracy and the timeliness of fault identification. To demonstrate the effectiveness of our framework, we conduct experiments on three types of open-source datasets relevant to PdM: electrical data, bearing datasets, and data from water circulation experiments.

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—a recent deep learning alternative to Multilayer Perceptrons. The proposed method automatically selects the most relevant features from sensor data and searches for optimal hyper-parameters within a single unified approach. By using shallow network architectures and fewer features, the resulting models are lightweight, easily interpretable, and practical for real-time applications. 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 availability of symbolic representations provided 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.

JaxKAN is a JAX-based library for building and training Kolmogorov-Arnold Networks (KANs) (

Particulate matter (PM) pollution is a major global concern due to its negative impact on human health. To effectively address this issue, it is crucial to have a reliable and efficient forecasting system. In this study, we propose a framework for predicting particulate matter concentrations by utilizing publicly available data from low-cost sensors and deep learning. We model the temporal variability through a novel Long Short-Term Memory Neural Network that offers a level of interpretability. The spatial dependence of particulate matter pollution in urban areas is modeled by incorporating characteristics of the urban agglomeration, namely, mean population density and mean floor area ratio. Our approach is general and scalable, as it can be applied to any type of sensor. Moreover, our framework allows for portable sensors, either mounted on vehicles or used by people. We demonstrate its effectiveness through a case study in Greece, where dense urban environments combined with low cost sensor networks is a peculiarity. Specifically, we consider Patras, a Greek port city, where the net PM pollution comes from a variety of sources, including traffic, port activity and domestic heating. Our model achieves a forecasting accuracy comparable to the resolution of the sensors and provides meaningful insights into the results.