# Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability

arXiv: https://arxiv.org/abs/2606.12658 · HTML: https://mlsanity.com/paper/2606.12658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks](https://mlsanity.com/paper/2202.01723/) (2022)
- [CMINNs: Compartment Model Informed Neural Networks -- Unlocking Drug Dynamics](https://mlsanity.com/paper/2409.12998/) (2024)
- [Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks](https://mlsanity.com/paper/2404.08019/) (2024)
- [PBPK-iPINNs: Inverse Physics-Informed Neural Networks for Physiologically Based Pharmacokinetic Brain Models](https://mlsanity.com/paper/2509.12666/) (2025)
- [Discovering intrinsic multi-compartment pharmacometric models using Physics Informed Neural Networks](https://mlsanity.com/paper/2405.00166/) (2024)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.