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.
翻译:不同方程式在现代世界发挥着关键作用,从科学、工程、生态、生态、经济和金融等科学、工程、生态、经济和金融等,可以用来模拟许多物理系统和过程。在本文中,我们研究使用物理知情神经网络(PINNs)在人体系统中药物同化的两种数学模型。在第一个模型中,我们考虑单剂量药物在人体系统中的情况,在第二个模型中,我们考虑这种药物的定期间隔过程。我们用区划图来模拟这些病例。由此产生的差异方程式使用PINN来解决。我们用PINN作为功能对等器提供前方多层透视器,而网络参数则根据最小的错误进行调整。此外,通过在网络参数中找到误差函数的梯度,对网络进行培训。我们利用PINNs Python图书馆DeepXDE(一个PINs Python 图书馆) 来解决描述药物同化两种模型的同步第一顺序差异方程式。结果显示,精确的解决方案和预测的解决方案之间的精确度很高,因为第一个模型和任何动态解算系统的第二个模型的第二个模型使用率达到10°(P11)。