Modelling Pharmacokinetic Variability with Physics-Informed Neural Networks

In many studies, individual measurements of a state variable are not reported; instead, summary statistics such as the mean and variance are provided. This is common in pharmacokinetic studies, where concentration–time profiles are often summarized across subjects. To incorporate this aggregated information into parameter estimation, we propose a methodology that leverages Physics-Informed Neural Networks (PINNs) [1] to learn the parameters of a predefined distribution. Our approach compares the differentials of the mean and variance obtained via automatic differentiation of the neural network (NN) with those derived analytically from the underlying ordinary differential equation (ODE) system through sampling, enabling the propagation of inference process.