A physics-guided hybrid model for core body temperature estimation: Thermoregulation model with residual learning

Accurate, non invasive estimation of core body temperature (Tc) is vital for real time physiological monitoring and heat illness prevention, yet gold standard measurements are invasive and impractical for wearables. We propose a physics guided hybrid framework that embeds a two node thermoregulation model within a neural residual learning pipeline. The physical layer uses heart rate (HR) to estimate metabolic heat production and directly incorporates wearable head skin temperature, while the residual learner (1D-CNN/LSTM/GRU) corrects systematic model discrepancies. Evaluated on a controlled dataset with strict participant-level splits, the Hybrid-CNN (full input) achieved the best overall accuracy (RMSE (Formula presented) ∘C, MAE (Formula presented) ∘C, (Formula presented) ), outperforming CNN/LSTM/GRU-only networks, an Extended Kalman Filter (RMSE (Formula presented) ∘C), and a physics-only baseline (RMSE (Formula presented) ∘C, negative R2). A simplified Hybrid-CNN that omits ambient sensors performed similarly (RMSE (Formula presented) ∘C, (Formula presented) ), indicating deployability with just HR and skin temperature. Noise robustness tests, conducted by injecting Gaussian noise into HR ((Formula presented) -50 bpm), showed Hybrid-CNN leading for σ ≤ 20 bpm, whereas Hybrid-LSTM was most resilient under extreme noise ((Formula presented) bpm; RMSE (Formula presented) ∘C). The residual learners are lightweight (120-140 KB; 250k-700k FLOPs/step), supporting real-time, on-device inference. Overall, coupling interpretable thermophysiology with targeted residual learning yields accurate, robust, and computationally efficient Tc monitoring for wearable health systems.