SiMBA-Augmented Physics-Informed Neural Networks for Industrial Remaining Useful Life Prediction

Remaining useful life (RUL) prediction of industrial equipment is critical for achieving safe operations and optimizing predictive maintenance. To tackle the limitations of poor interpretability, inaccurate predictions, and high computational cost in complex system degradation modeling, this paper proposes SiMBA-PINN, a novel fusion framework that synergizes Physics-Informed Neural Network (PINN) with an enhanced state-space model (SiMBA). The framework achieves dynamic fusion of data-driven features and physical laws through a two-branch synergistic mechanism: the temporal modeling branch combines selective state-space SiMBA with Einstein Fast Fourier Transform (EinFFT)-based spectral mixing to efficiently capture cross-sensor temporal dependencies and degradation trends, while the physics-constraint branch embeds automatically differentiable partial differential equation residuals derived from domain-specific degradation mechanisms, enforcing physical consistency through deep hidden physics modeling. Here, the EinFFT-based spectral mixing leverages frequency-domain interactions to effectively blend the spectral components of multivariate time-series data, thereby enhancing the modeling of cross-sensor dependencies. Meanwhile, deep hidden physics modeling integrates physics-informed partial differential equation (PDE) residuals through differentiable operators, aligning the learned representations with domain-specific dynamics via a constraint-driven loss design. Experimental results from the C-MAPSS dataset confirm that the proposed model significantly outperforms PINN-, Mamba- and attention mechanism-based models, achieving State-of-the-Art RMSE on the most challenging FD004 subset. This physics-aware framework achieves deployable and interpretable RUL prediction by balancing accuracy with linear-time complexity.