Charuka D. Wickramasinghe

Charuka D. Wickramasinghe, Krishanthi C. Weerasinghe, Pradeep K. Ranaweera

Physics-Informed Neural Networks (PINNs) leverage machine learning with differential equations to solve direct and inverse problems, ensuring predictions follow physical laws. Physiologically based pharmacokinetic (PBPK) modeling advances beyond classical compartmental approaches by using a mechanistic, physiology focused framework. A PBPK model is based on a system of ODEs, with each equation representing the mass balance of a drug in a compartment, such as an organ or tissue. These ODEs include parameters that reflect physiological, biochemical, and drug-specific characteristics to simulate how the drug moves through the body. In this paper, we introduce PBPK-iPINN, a method to estimate drug-specific or patient-specific parameters and drug concentration profiles in PBPK brain compartment models using inverse PINNs. We demonstrate that, for the inverse problem to converge to the correct solution, the loss function components (data loss, initial conditions loss, and residual loss) must be appropriately weighted, and parameters (including number of layers, number of neurons, activation functions, learning rate, optimizer, and collocation points) must be carefully tuned. The performance of the PBPK-iPINN approach is then compared with established traditional numerical and statistical methods.

Tyrus Whitman, Andrew Particka, Christopher Diers et al.

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations (ODEs). While traditional numerical methods a re effective for many ODEs, they often struggle to achieve convergence in problems involving high stiffness, shocks, irregular domains, singular perturbations, high dimensions, or boundary discontinuities. Alternatively, PINNs offer a powerful approach for handling challenging numerical scenarios. In this study, classical ODE problems are employed as controlled testbeds to systematically evaluate the accuracy, training efficiency, and generalization capability under controlled conditions of the PINNs framework. Although not a universal solution, PINNs can achieve superior results by embedding physical laws directly into the learning process. We first analyze the existence and uniqueness properties of several benchmark problems and subsequently validate the PINNs methodology on these model systems. Our results demonstrate that for complex problems to converge to correct solutions, the loss function components data loss, initial condition loss, and residual loss must be appropriately balanced through careful weighting. We further establish that systematic tuning of hyperparameters, including network depth, layer width, activation functions, learning rate, optimization algorithms, w eight initialization schemes, and collocation point sampling, plays a crucial role in achieving accurate solutions. Additionally, embedding prior knowledge and imposing hard constraints on the network architecture, without loss the generality of the ODE system, significantly enhances the predictive capability of PINNs.