Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations

Researchers introduce PC-MambaSDE, a machine learning framework designed to predict remaining useful life in industrial equipment by combining continuous-time neural networks with physics-based constraints. The model handles irregular sensor data and prevents physically impossible degradation patterns, outperforming existing methods especially when observation data is sparse.

PC-MambaSDE addresses a critical gap in predictive maintenance technology by solving two interconnected problems: handling real-world messy sensor data and preventing AI models from generating physically nonsensical predictions. Industrial sensors rarely report at regular intervals and frequently have missing data points, yet existing models treat these irregularities as noise rather than exploiting them as information. This research bridges classical physics and modern deep learning by embedding monotonic degradation constraints—the fact that equipment damage only accumulates, never reverses—directly into the neural architecture rather than applying it post-hoc.

The framework's innovation lies in its theoretical rigor and practical engineering. The authors prove their approach minimizes KL divergence through Girsanov's theorem and guarantee stable learned dynamics using Lyapunov analysis, transforming an ad-hoc engineering problem into a mathematically grounded optimization problem. By formulating RUL prediction as a boundary value problem with terminal degradation penalties, the model learns to guide equipment trajectories toward failure states in physically consistent ways.

For industrial operators, this matters significantly. Inaccurate RUL predictions either cause premature equipment replacement (wasted capital) or catastrophic failures (operational risk). The model's superior performance under extreme data scarcity directly addresses deployment scenarios where sensors fail or operate intermittently. This work demonstrates how domain knowledge from physics can substantially improve AI reliability without requiring larger datasets or more computational resources.

Future research likely explores application to different equipment types and integration with edge computing systems for real-time deployment in resource-constrained industrial environments.

• →PC-MambaSDE combines continuous-time neural networks with physics constraints to predict equipment failure with higher accuracy under irregular sensor data.
• →The framework enforces monotonic degradation trajectories, preventing AI models from generating physically impossible equipment states.
• →Mathematical proof of equivalence to KL divergence minimization and Lyapunov stability analysis provides theoretical guarantees for the learned dynamics.
• →Performance improvements are most pronounced under extreme observation scarcity, directly addressing real-world industrial deployment challenges.
• →The hybrid irregularity generation scheme enables rigorous evaluation that simulates authentic industrial sensor imperfections rather than artificial missing data patterns.