# Study of Drug Assimilation in Human System using Physics Informed Neural Networks

arXiv: https://arxiv.org/abs/2110.05531 · HTML: https://mlsanity.com/paper/2110.05531/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 8 Oct 2021.

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

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [A Discussion on Solving Partial Differential Equations using Neural Networks](https://mlsanity.com/paper/1904.07200/) (2019)
- [dNNsolve: an efficient NN-based PDE solver](https://mlsanity.com/paper/2103.08662/) (2021)
- [Deep Neural Network Based Differential Equation Solver for HIV Enzyme Kinetics](https://mlsanity.com/paper/2102.08471/) (2021)

## Built on by (most cited first, 3 of 3)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)

## Abstract (arXiv)

Differential equations play a pivotal role in modern world ranging from science, engineering, ecology, economics and finance where these can be used to model many physical systems and processes. In this paper, we study two mathematical models of a drug assimilation in the human system using Physics Informed Neural Networks (PINNs). In the first model, we consider the case of single dose of drug in the human system and in the second case, we consider the course of this drug taken at regular intervals. We have used the compartment diagram to model these cases. The resulting differential equations are solved using PINN, where we employ a feed forward multilayer perceptron as function approximator and the network parameters are tuned for minimum error. Further, the network is trained by finding the gradient of the error function with respect to the network parameters. We have employed DeepXDE, a python library for PINNs, to solve the simultaneous first order differential equations describing the two models of drug assimilation. The results show high degree of accuracy between the exact solution and the predicted solution as much as the resulting error reaches10^(-11) for the first model and 10^(-8) for the second model. This validates the use of PINN in solving any dynamical system.