Abstract
We develop an approach to estimate a blood alcohol signal from a transdermal alcohol signal using physics-informed neural networks (PINNs). Specifically, we use a generative adversarial network (GAN) with a residual-augmented loss function to estimate the distribution of unknown parameters in a diffusion equation model for transdermal transport of alcohol in the human body. We design another PINN for the deconvolution of the blood alcohol signal from the transdermal alcohol signal. Based on the distribution of the unknown parameters, this network is able to estimate the blood alcohol signal and quantify the uncertainty in the form of conservative error bands. Finally, we show how a posterior latent variable can be used to sharpen these conservative error bands. We apply the techniques to an extensive dataset of drinking episodes and demonstrate the advantages and shortcomings of this approach.