A Hybrid Probabilistic Framework for Temporal Drift Compensation in Conductimetric Biosensors: Combining Machine Learning Predictions with Bayesian Latent Process Modeling

This work aims to study and improve the long-term stability of conductimetric biosensors for urea detection in clinical and environmental samples, which are fundamentally limited by complex thermal and temporal drifts due to temperature-sensitive enzyme kinetics, variations in ionic mobility, and the progressive degradation of the sensing layer. The biosensor targets the urea concentration range 0.01–30 mM, validated against experimental data and covering the clinically relevant range for blood urea detection (2.5–7.5 mM), urine (20–40 mM), and environmental monitoring applications. Conventional calibration techniques, such as the conventional calibration method (based on reference measurements), and purely deterministic correction methods, such as deterministic methods (based on known fixed equations), often prove insufficient because they struggle to capture the non-stationary and inherently stochastic nature of these drifts. In this work, we propose an original hybrid probabilistic framework that synergistically combines machine learning and Bayesian inference for robust adaptive drift compensation. A Random Forest model is first implemented to model the deterministic nonlinear relationships between environmental parameters (temperature, pH, CO2 concentration) and the sensor response. The residual temporal drift is then explicitly modeled as a non-stationary latent stochastic process using Bayesian inference based on a Gaussian process. This approach allows continuous online model updating, real-time uncertainty quantification, and automatic detection of anomalies. The models were trained and validated on a large dataset obtained from multiphysics simulations carried out in COMSOL Multiphysics 5.6. These simulations incorporated enzymatic reactions, thermal effects, and chemical dynamics taking place inside the sensor. Experimental results show that the hybrid approach substantially enhances sensor performance, lowering the root mean square error (RMSE) to below 0.8 μS/cm (corresponding to less than 0.5% of the full-scale response) over a wide temperature range (15–45 °C) and across extended operating periods. This represents a clear improvement over conventional compensation method. By merging the predictive power of ensemble learning with a probabilistic Bayesian model of dynamic drift, this study introduces a fresh perspective on the design of intelligent, self-adaptive, and drift-resistant conductimetric biosensors. The proposed framework holds strong potential for reliable, long-term autonomous operation in urea reliable, long-term autonomous operation in urea monitoring across biomedical diagnostics (kidney/liver function assessment) and environmental surveillance (water eutrophication prevention).