The problem of estimating breath alcohol concentration based on transdermal alcohol biosensor data is considered. Transdermal alcohol concentration provides a promising alternative to classical methods such as breathalyzers or drinking diaries. A physics-informed long Short-term memory (LSTM) network with covariates for the solution of the estimation problem is developed. The data-driven nature of an LSTM is augmented with a first principles physics-based population model for the diffusion of ethanol through the epidermal layer of the skin. The population model in an abstract parabolic framework appears as part of a regularization term in the loss function of the LSTM. While learning, the model is encouraged to both fit the data and to produce physically meaningful outputs. To deal with the high variation observed in the data, a mechanism for the uncertainty quantification of the estimates based on a recently discovered relation between Monte-Carlo dropout and Bayesian learning is used. The physics-based population model and the LSTM are trained and tested using controlled laboratory collected breath and transdermal alcohol data collected in four sessions from 40 orally dosed participants (50% female, ages 21 - 33 years, 35% BMI above 25.0) resulting in 256 usable drinking episodes partitioned into training and testing sets. Body measurement (e.g. BMI, hip to waist ratio, etc.), personal (e.g. sex, age, race, etc.), drinking behavior (e.g. frequent, rarely, etc.), and environmental (e.g. temperature, humidity, etc.) covariates were also collected from participants. The importance of various covariates in the estimation is investigated using Shapley values. It is shown that the physics-informed LSTM network can be successfully applied to drinking episodes from both the training and test set, and that the physics-based information leads to better generalization ability on new drinking episodes with the uncertainty quantification yielding credible bands that effectively capture the true signal. Compared to two machine learning models from previous studies, the proposed model reduces relative error in estimated breath alcohol concentration by 58% and 72%, and relative peak error by 33% and 76%.
