A Framework for Parameter Estimation and Uncertainty Quantification in Systems Biology Using Quantile Regression and Physics-Informed Neural Networks.

Journal: Bulletin of mathematical biology
PMID:

Abstract

A framework for parameter estimation and uncertainty quantification is crucial for understanding the mechanisms of biological interactions within complex systems and exploring their dynamic behaviors beyond what can be experimentally observed. Despite recent advances, challenges remain in achieving the high accuracy of parameter estimation and uncertainty quantification at moderate computational costs. To tackle these challenges, we developed a novel approach that integrates the quantile method with Physics-Informed Neural Networks (PINNs). This method utilizes a network architecture with multiple parallel outputs, each corresponding to a distinct quantile, facilitating a comprehensive characterization of parameter estimation and its associated uncertainty. The effectiveness of the proposed approach was validated across three study cases, where it was compared to the Monte Carlo dropout (MCD) and the Bayesian methods. Furthermore, a larger-scale model was employed to further demonstrate the excellent performance of the proposed approach. Our approach exhibited significantly superior efficacy in parameter estimation and uncertainty quantification. This highlights its great promise to broaden the scope of applications in system biology modeling.

Authors

  • Haoran Hu
    Department of Mathematics & Statistics, University of Massachusetts, Amherst, MA 01003, USA. Electronic address: haoranhu@umass.edu.
  • QianRu Cheng
    School of Computer Science and Engineering, North Minzu University, Yinchuan, 750021, China; Key Laboratory of Image and Graphics Intelligent Processing of State Ethnic Affairs Commission, North Minzu University, Yinchuan, 750021, China. Electronic address: chengqianru5@163.com.
  • Shuli Guo
    State Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing, 100081, China. Electronic address: guoshuli@bit.edu.cn.
  • Huifang Wen
    Department of Biomedical Engineering, Research Center for Nano-Biomaterials and Regenerative Medicine, College of Artificial Intelligence, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People's Republic of China.
  • Jing Zhang
    MOEMIL Laboratory, School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu, China.
  • Yongqi Song
    Department of Biomedical Engineering, Research Center for Nano-Biomaterials and Regenerative Medicine, College of Artificial Intelligence, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People's Republic of China.
  • Kaiqun Wang
    Department of Biomedical Engineering, Research Center for Nano-Biomaterials and Regenerative Medicine, College of Artificial Intelligence, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People's Republic of China. wangkaiqun@tyut.edu.cn.
  • Di Huang
    Centre for Ophthalmology and Visual Science (incorporating Lions Eye Institute), The University of Western Australia, Perth, Western Australia, Australia.
  • Hui Zhang
    Department of Pulmonary Vessel and Thrombotic Disease, Sixth Medical Center, Chinese PLA General Hospital, Beijing, China.
  • Chaofeng Zhang
    Sino-Jan Joint Lab of Natural Health Products Research, School of Traditional Chinese Medicines, China Pharmaceutical University, Nanjing 210009, China; Department of Chinese Medicine Resources, School of Traditional Chinese Medicines, China Pharmaceutical University, Nanjing 210009, China. Electronic address: zhangchaofeng@cpu.edu.cn.
  • Yanhu Shan
    School of Instrument and Electronics, North University of China, Taiyuan, 030051, Shanxi, People's Republic of China. shanyanhu@nuc.edu.cn.