Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for applying deep neural networks to solve partial differential equations (PDEs). However, accurately addressing challenging regions in the solutions of stiff PDEs necessitates adaptive methods. Additionally, the inherent limitations of baseline PINN in handling sequential or time-series data significantly constrain their applicability. In light of this, this paper introduces a Self-Adaptive Physics-Informed Attention-based Gated Recurrent Unit (SA-PI-AGRU) model, which enhances the baseline PINN framework to address these critical issues. The proposed SA-PI-AGRU model advances PINNs by integrating an attention-based GRU layer, which is particularly effective at analyzing sequential data. This dual objective of minimizing losses while optimizing the weighting parameters ensures a robust training and testing process, which can be used for many applications, including language modelling and text generation, prognostics and health management, and other prediction/forecasting problems. The efficacy of the SA-PI-AGRU model is demonstrated through an essential case study, which is to predict the state of health (SoH) of lithium-ion batteries (LIBs), utilizing four different battery datasets from the National Aeronautics and Space Administration (NASA). The obtained results suggest significant improvements in predictive accuracy and network initialization capabilities compared to the baseline PINN and other benchmark models.

Electric vehicles (EVs) are playing a pivotal role in transportation systems to conform to the rising exigencies for enhanced performance with safety and hindered environmental impact. Thus, to improve the efficiency and downsize the maintenance cost of EVs, an early fault diagnosis (FD) framework is crucial. Bearing and stator winding faults, which account for approximately 78% of induction machine (IM) incipient faults in EVs, remain rather elusive for conventional sensors to accurately classify them and their incipient values. To this end, this paper presents a novel Attention-enhanced Autoencoder-Gated Recurrent Unit (AAGRU) model that improves the accuracy and efficiency of fault analysis in IMs. Moreover, since bearing faults are usually captured through vibration sensors, which are expensive and require direct coupling with the IM, a hybrid signal re-constructor is devised based on merely stator current signals. The proposed model leverages Empirical Mode Decomposition (EMD), Fast Fourier Transform (FFT), and Discrete Wavelet Decomposition (DWT) to process the electric current data, which are then used by the AAGRU model to identify, detect, and classify the fault patterns. Experimental results demonstrate that the proposed model offers a 6%-20% improvement in fault detection and an 8%-28% improvement in inter-turn shortcircuit fault severity classification relative to different shallow and deep-based benchmark models. The proposed model was also tested on different load conditions to ensure its applicability in practice.