TFMPINN: a meta-learning approach for remaining useful life prediction via time-domain latent encoding and frequency-domain physics-informed neural networks

Remaining useful life (RUL) prediction of aero-engines plays a critical role in ensuring operational safety and guiding maintenance decision-making. Although data-driven approaches have achieved remarkable progress in recent years, existing models still face challenges such as insufficient cross-task generalisation, lack of physical consistency, and limited interpretability in the prediction process. This paper proposes a meta-learning framework for lifetime prediction (TFMPINN) that integrates time-domain latent state modelling with a frequency-domain physics-informed neural network. Specifically, a Temporal State Modelling Encoder (TSME) is constructed to build a continuous latent space via reparameterization, enabling capture of key dynamic features and uncertainty throughout the degradation process. Besides, the Fourier Physics-Constrained Network (FPCN) is designed to encode frequency-domain physical priors by introducing implicit PDE residual constraints, enhancing the model’s ability to capture consistent degradation dynamics, while an Adaptive Weighted Channels (AWC) module in the predictor adaptively fuses multi-sensor degradation features. By incorporating a meta-learning mechanism optimised over task distributions, the framework achieves rapid adaptation and improved generalisation under few-shot and varying operating conditions. Experiments on NASA C-MAPSS and N-CMAPSS turbofan engine datasets demonstrate that TFMPINN outperforms existing methods in prediction accuracy, cross-task generalisation, and interpretability of the degradation process.