Physics-informed weighted Ramos–Louzada model: integrating statistical and physical constraints for survival analysis

The paper proposes a new physics-informed, weighted length-biased Ramos–Louzada (WLBRL) system for survival and reliability analysis, combining statistical inference with physical constraints. The suggested WLBRL distribution explicitly corrects for length-biased sampling, and physics-informed neural networks (PINNs) impose relationships on survival hazards in estimation that are implicitly defined by differential equations. The physics-informed maximum likelihood estimation approach is presented to stabilize parameter inference under noisy, limited data. Vast simulation literature and real-world medical and engineering data have shown that the proposed framework reduces mean squared error by 40% compared to the classical Ramos–Louzada (RL), Weibull, and exponential models. These findings verify that integrating physical laws into weighted survival models enhances estimation accuracy, robustness, and explainability, indicating that the weighted length-biased Ramos–Louzada physics-informed neural network (WLBRL-PINN) system is generally applicable to uncertainty-aware risk assessment in biomedical and engineering systems.