# CMINNs: Compartment Model Informed Neural Networks -- Unlocking Drug Dynamics

arXiv: https://arxiv.org/abs/2409.12998 · HTML: https://mlsanity.com/paper/2409.12998/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 87 references that are in the map.
- First posted on arXiv 19 Sep 2024.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [State-space models are accurate and efficient neural operators for dynamical systems](https://mlsanity.com/paper/2409.03231/) (2024)
- [Physics-Informed Neural Networks and Extensions](https://mlsanity.com/paper/2408.16806/) (2024)
- [Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks](https://mlsanity.com/paper/2404.08019/) (2024)
- [Pharmacokinetic/Pharmacodynamic Anesthesia Model Incorporating psi-Caputo Fractional Derivatives](https://mlsanity.com/paper/2311.05715/) (2023)

## Built on by (most cited first, 7 of 7)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.05230/) (2026)
- [Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology](https://mlsanity.com/paper/2504.07379/) (2025)
- [Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines](https://mlsanity.com/paper/2602.19265/) (2026)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design](https://mlsanity.com/paper/2505.20300/) (2025)
- [Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability](https://mlsanity.com/paper/2606.12658/) (2026)

## Abstract (arXiv)

In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug absorption, distribution, and their impact on targets. Although multi-compartment models are frequently utilized to elucidate intricate drug dynamics, they can also be overly complex. To generalize modeling while maintaining simplicity, we propose an innovative approach that enhances PK and integrated PK-PD modeling by incorporating fractional calculus or time-varying parameter(s), combined with constant or piecewise constant parameters. These approaches effectively model anomalous diffusion, thereby capturing drug trapping and escape rates in heterogeneous tissues, which is a prevalent phenomenon in drug dynamics. Furthermore, this method provides insight into the dynamics of drug in cancer in multi-dose administrations. Our methodology employs a Physics-Informed Neural Network (PINN) and fractional Physics-Informed Neural Networks (fPINNs), integrating ordinary differential equations (ODEs) with integer/fractional derivative order from compartmental modeling with neural networks. This integration optimizes parameter estimation for variables that are time-variant, constant, piecewise constant, or related to the fractional derivative order. The results demonstrate that this methodology offers a robust framework that not only markedly enhances the model's depiction of drug absorption rates and distributed delayed responses but also unlocks different drug-effect dynamics, providing new insights into absorption rates, anomalous diffusion, drug resistance, peristance and pharmacokinetic tolerance, all within a system of just two (fractional) ODEs with explainable results.