Why Physics-Informed Neural Networks Fail on Stiff Drug Dynamics, and How to Fix Them (Spring 2027)

When a patient in intensive care receives an antibiotic, the dose must keep the drug level high enough to kill the infection but low enough to spare the kidneys. Every patient absorbs and clears the drug at a different rate, and doctors usually have only a handful of noisy blood samples from which to work out those rates. The standard approach fits

the model by solving the differential equations repeatedly inside an optimization loop, which works well when the model is fully specified. Physics-informed neural networks (PINNs) offer a complementary route: they fit the blood samples and the governing equations in a single training run, treat the unknown rates as learnable parameters, and extend naturally to models that are only partly known. But drug dynamics are stiff, with absorption over minutes and clearance over hours, and PINNs are known to struggle on stiff equations.

This project asks a simple question: when drug dynamics are stiff, can a PINN still recover a patient's absorption and elimination rates from a few blood samples, and if not, what fixes it? Early results suggest the answer is subtle, since a PINN can fit the blood samples well yet still return the wrong rates.

For more information contact Farjana Siddiqua (siddiqua@iastate.edu)

People:

• Farjana Siddiqua (Postdoc)

• TBD

Pre-requisites:

• The mathematics needed is exactly Calculus 1–3, differential equations and linear algebra.

• The only extra requirement is basic Python (that could be learned or you can use open sources).