Physics-Informed Neural Networks vs. Physics Models for Non-Invasive Glucose Monitoring: A Comparative Study Under Noise-Stressed Synthetic Conditions

Non-invasive glucose monitoring outside controlled settings is dominated by low signal-to-noise ratio (SNR): hardware drift, environmental variation, and physiology suppress the glucose signature in NIR signals. We present a noise-stressed NIR simulator that injects 12-bit ADC quantisation, LED drift, photodiode dark noise, temperature/humidity variation, contact-pressure noise, Fitzpatrick I-VI melanin, and glucose variability to create a low-correlation regime (rho_glucose-NIR = 0.21). Using this platform, we benchmark six methods: Enhanced Beer-Lambert (physics-engineered ridge regression), Original PINN, Optimised PINN, RTE-inspired PINN, Selective RTE PINN, and a shallow DNN. The physics-engineered Beer Lambert model achieves the lowest error (13.6 mg/dL RMSE) with only 56 parameters and 0.01 ms inference, outperforming deeper PINNs and the SDNN baseline under low-SNR conditions. The study reframes the task as noise suppression under weak signal and shows that carefully engineered physics features can outperform higher-capacity models in this regime.

💡 Research Summary

The paper tackles the fundamental challenge of non‑invasive glucose monitoring: the extremely low signal‑to‑noise ratio (SNR) encountered in real‑world settings. To study this problem under controlled yet realistic conditions, the authors build a comprehensive synthetic near‑infrared (NIR) simulator that injects twelve sources of noise and variability: 12‑bit ADC quantisation, LED intensity drift and ageing, photodiode dark current, shot and thermal noise, temperature‑dependent drift, relative humidity effects, contact‑pressure fluctuations, Fitzpatrick I‑VI skin melanin levels, skin thickness, blood perfusion, and hydration changes. By combining these factors, the simulator reduces the correlation between glucose concentration and NIR spectra from the laboratory value of ≈0.82 down to ≈0.21, matching values reported for early field prototypes.

Using this low‑correlation dataset, six model families are benchmarked under identical conditions: (1) an Enhanced Beer‑Lambert (EBL) model that extracts 56 physics‑derived features (log‑absorbance, wavelength differences, log‑ratios, and personalized physiological weighting) and applies ridge regression; (2) a “Original” PINN that enforces Beer‑Lambert residuals as a soft loss term; (3) an Optimised PINN with deeper architecture and stronger regularisation; (4) an RTE‑inspired PINN that adds a lightweight radiative‑transfer‑equation (RTE) regulariser to capture scattering; (5) a Selective RTE PINN that limits the physics scope for computational efficiency; and (6) a shallow deep neural network (SDNN) that relies purely on data without any physics constraints.

The experimental results are striking. The EBL model achieves the lowest root‑mean‑square error (RMSE) of 13.6 mg/dL, requires only 56 trainable parameters, and runs inference in 0.01 ms on an embedded processor. In contrast, the PINN variants, despite having many more parameters, either over‑fit the imperfect physics (when the physics loss weight λ is too high) or suffer from high computational load (especially the full RTE formulation). Their RMSE values are consistently higher than the EBL baseline, and inference times are an order of magnitude longer. The shallow DNN, lacking any physics guidance, also performs worse, with RMSE exceeding 20 mg/dL and similar latency to the PINNs.

The authors interpret these findings as evidence that, in a noise‑dominated regime, carefully engineered physics‑based features combined with a simple linear model can outperform sophisticated neural architectures. The physics constraints in PINNs are only beneficial when the governing equations accurately describe the measurement process; under realistic tissue scattering and hardware drift, the Beer‑Lambert and RTE approximations are imperfect, and the added regularisation can misguide learning. Moreover, the study reframes non‑invasive glucose sensing as a noise‑suppression problem rather than a pure regression task, emphasizing the importance of robust feature design.

Beyond the comparative analysis, the paper contributes a publicly released simulation framework (GitHub link provided) that can serve as a benchmark for future work on wearable optical sensors. The authors acknowledge that real‑world deployments may introduce additional complexities—such as sensor‑skin misalignment, sweat, hair, dynamic tissue hydration, and long‑term population drift—that are not captured in the current simulator. Nonetheless, the work demonstrates that, for low‑SNR optical biosensing, “physics‑engineered linear regression” is a highly competitive, interpretable, and deployment‑ready solution, while more complex PINN architectures require further refinement to justify their computational cost.