Stochastic Physics-Informed Neural Networks for Solving Drug Transport Equations with Uncertain Inputs

Stochastic PINN for Solving Drug Transport Equations with Uncertain Inputs

Abstract

Accurate modeling of drug transport in biological tissues is essential for optimizing therapeutic
strategies. However, traditional numerical methods such as finite differences or finite elements become
computationally expensive and inefficient when accounting for uncertainties in physiological
parameters, including diffusion coefficients, reaction rates, and tissue heterogeneity. In this work,
we employ Physics-Informed Neural Networks (sPINN) as a direct solver for drug transport equations
with random coefficients, thereby replacing conventional discretization-based approaches.
The governing partial differential equations are embedded into the neural network loss function,
which allows the model to enforce physical laws throughout the training process. Once trained,
the sPINN is combined with Monte Carlo sampling to estimate statistical quantities of interest,
such as means, variances, and confidence intervals, under different realizations of uncertain
parameters. Numerical results show that the proposed method achieves accuracy comparable
to reference solutions while significantly reducing computational cost. This hybrid framework,
combining sPINN with Monte Carlo estimation, offers a robust and data-efficient approach for
modeling drug distribution in complex biological environments under uncertainty.