Estimating the evolution of the battery's State of Charge (SoC) in response to its usage is critical for implementing effective power management policies and for ultimately improving the system's lifetime. Most existing estimation methods are either physics-based digital twins of the battery or data-driven models such as Neural Networks (NNs). In this work, we propose two new contributions in this domain. First, we introduce a novel NN architecture formed by two cascaded branches: one to predict the current SoC based on sensor readings, and one to estimate the SoC at a future time as a function of the load behavior. Second, we integrate battery dynamics equations into the training of our NN, merging the physics-based and data-driven approaches, to improve the models' generalization over variable prediction horizons. We validate our approach on two publicly accessible datasets, showing that our Physics-Informed Neural Networks (PINNs) outperform purely data-driven ones while also obtaining superior prediction accuracy with a smaller architecture with respect to the state-of-the-art.

In an industrial CPS scenario, the most crucial resource is the availability of data reflecting the different aspects of production. Detecting complex anomalies on massive amounts of data is a crucial Such data consist of multiple interdependent variables rapidly evolving task in Industry 4.0, best addressed by deep learning. However, over time, thus falling under the typical definition of Multivariate available solutions are computationally demanding, requiring cloud Time Series (MTS) [14]. After collection, the time series, originated architectures prone to latency and bandwidth issues. This work by heterogeneous sensors and data sources, are integrated presents VARADE, a novel solution implementing a light autoregressive through Industrial Internet of Things (IIoT) technologies and made framework based on variational inference, which is best available for anomaly detection, visualization, and analysis [27].

Industry 4.0 involves the integration of digital technologies, such as IoT, Big Data, and AI, into manufacturing and industrial processes to increase efficiency and productivity. As these technologies become more interconnected and interdependent, Industry 4.0 systems become more complex, which brings the difficulty of identifying and stopping anomalies that may cause disturbances in the manufacturing process. This paper aims to propose a diffusion-based model for real-time anomaly prediction in Industry 4.0 processes. Using a neuro-symbolic approach, we integrate industrial ontologies in the model, thereby adding formal knowledge on smart manufacturing. Finally, we propose a simple yet effective way of distilling diffusion models through Random Fourier Features for deployment on an embedded system for direct integration into the manufacturing process. To the best of our knowledge, this approach has never been explored before.