Hyperspectral anomaly detection (HAD) remains a critical challenge in remote sensing, aiming to precisely separate sparse, unknown anomalies from complex, high-proportion backgrounds. Although deep learning architectures, particularly the Transformer, dominate HAD, their effectiveness is constrained by two fundamental deficiencies: the architectural flaw of “uniform processing” across feature tokens and the microscopic reliance on fixed non-linear activation functions, which are mathematically insufficient for modeling the complex HSI spectral features. To address this dual challenge, this paper introduces the Synergistic Kolmogorov–Arnold Network and Fidelity-Gated Transformer (KANGT) framework. This novel framework integrates two synergistic innovations: the Fidelity-Gated Context-Aware Transformer (GCAT), which employs a reconstruction fidelity-based gating module named the Contextual Feature Matching Module (CFMM) to explicitly and dynamically separate background and anomaly processing streams, and the KAN-MLP module, which replaces traditional Feed-Forward Networks (FFNs) with learnable, spline-based functions, enabling superior adaptive non-linear feature approximation. Extensive experiments on challenging real-world HSI datasets consistently demonstrate KANGT’s superior performance compared to existing methods, and the average AUC reached 0.9921 on eight datasets. This work establishes a robust new paradigm for HAD, with future efforts aimed at optimizing the computational efficiency of KANs to meet real-time application demands.

Accurate and reliable state of health (SOH) estimation is essential for lithium-ion battery safety and lifetime management. Physics-informed neural networks (PINNs) integrate battery degradation knowledge with deep learning to improve the physical consistency of SOH estimation. However, existing PINNs insufficiently capture degradation evolution across consecutive cycles and show limited applicability across battery chemistries and charge/discharge protocols. To address these issues, we propose a sequence-conditioned physics-informed neural network (SC-PINN) that uses a gated recurrent unit (GRU) to encode local degradation states and incorporates a degradation dynamics consistency constraint and a monotonic degradation prior to improve prediction accuracy and physical plausibility. We also develop a general charging feature extraction method for different battery chemistries and charge/discharge protocols, extracting unified 18-dimensional health features from charging segments at high state of charge (SOC). The method is validated using 317 batteries and 197,024 valid cycle samples covering four battery chemistries across nine representative tasks. SC-PINN achieves a mean absolute percentage error (MAPE) of 0.6285% and a root mean square error (RMSE) of 0.8924%, with the lowest RMSE in eight of nine tasks. Compared with other methods, the proposed method demonstrates good stability and applicability in both standard and small-sample experiments.