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.

Remaining Useful Life (RUL) plays a critical role in prognostics and health management systems. It helps increase reliability and safety for the equipment used in the modern industry. The new idea proposed is the Mamba deep learning model, which aims to find a good balance between predictive performance and computation cost. This paper presents a multimodal RUL prediction model, Cau–BiMamba–LSTM, using causal discovery, a bidirectional Mamba (BiMamba), attention mechanism, and Long Short-Term Memory (LSTM). The framework utilizes maximum information transfer entropy and simple exponential smoothing in building a causal graph model that extracts groups of feature variable groupsLSTM performs long-range dependencies; the attention mechanism dynamically focuses attention according to the temporal context; finally, the bidirectional state space model captures all contextual information over time for a richer insight into underlying data patterns. Tests conducted on the C-MAPSS dataset confirm that this model achieves superior predictive accuracy and robustness. Moreover, the model achieves high predictive performance in very complex, long time–series and provides fast responses.