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

arXiv: https://arxiv.org/abs/2509.12253 · HTML: https://mlsanity.com/paper/2509.12253/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 2 of 2)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)

## Abstract (arXiv)

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.