应用物理信息神经研究药物在人体系统中的同化 网络

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摘要翻译：
微分方程在现代科学、工程、生态学、经济学和金融等领域发挥着举足轻重的作用，可以用来模拟许多物理系统和过程。本文利用物理信息神经网络（PINNs）研究了药物在人体系统中同化的两个数学模型。在第一个模型中，我们考虑了人体系统中单剂量药物的情况，在第二个模型中，我们考虑了这种药物在规则间隔内服用的过程。我们已经用隔间图对这些案例进行了建模。采用前馈多层感知器作为函数逼近器，并对网络参数进行最小误差调整，得到的微分方程用PINN进行求解。此外，通过寻找误差函数相对于网络参数的梯度来训练网络。我们使用PYNS的python库DeepXDE来求解描述两种药物同化模型的一阶微分方程组。结果表明，当第一个模型的误差达到10^(-11)，第二个模型的误差达到10^(-8)时，精确解与预测解之间的精度较高。这验证了PINN在求解任何动力系统中的应用。
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英文标题：
《Study of Drug Assimilation in Human System using Physics Informed Neural
  Networks》
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作者：
Kanupriya Goswami, Arpana Sharma, Madhu Pruthi, Richa Gupta
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最新提交年份：
2021
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
--

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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/2110.05531

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关键词：应用物理 Assimilation Differential Quantitative SIMULTANEOUS PINN 信息 研究 using 金融