Improving Physiological Modeling with Machine Learning

机器学习（ML）是解决许多社会挑战的重要工具。ML也是美国竞争力的关键因素。ML的大部分灵感来自生物学，有时旨在了解生物系统，特别是大脑。然而，ML的方法只是表面上类似于生物系统。理解生物系统是数学生物学（MB）的核心目标之一。MB通过仔细匹配实验数据和重建生物系统的生理学，采取了与ML看似相反的方法。到目前为止，ML和MB的工具主要是不同的。在这个项目中，主要研究者（PI）将寻求这两种不同方法之间的协同作用，并建立连接这两种方法的数学工具。PI还将开发工具来研究真实世界的昼夜节律和睡眠。其中一个工具是PI将部署的智能手机应用程序。PI还应通过向服务不足的高中推广，努力增加代表性不足的群体在数学方面的参与。本计画的数学模型包括常微分方程与随机微分方程。主要目标之一是基于神经元的生物病理学准确模型构建ML工具。这些模型将使用Hodgkin和Huxley开发的形式主义。这里要解决的关键问题是如何通过改进反向传播技术来学习高度非线性模型和时间依赖性。此外，PI将开发使用当前开发的模型预测的方法，以增强ML中的分类。如何对常微分方程模型的模拟结果进行分类，以及如何将不确定性合理地引入常微分方程模型，是本文要解决的关键问题。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

Machine learning (ML) is a crucial tool to address many societal challenges. ML is also a critical factor in American competitiveness. Much of ML was inspired by biology and sometimes aims to understand biological systems, especially the brain. Yet, the methodologies of ML resemble biological systems only superficially. Understanding biological systems is one of the central goals of Mathematical Biology (MB). MB takes a seemingly opposite approach to ML by carefully matching experimental data and reconstructing the physiology of biological systems. So far, the tools of ML and MB have been mainly distinct. In this project, the Principal Investigator (PI) will seek synergies between these two different methodologies and build mathematical tools that bridge these two approaches. PI will also develop tools to study real-world circadian rhythms and sleep. One tool is a smartphone app the PI will deploy. PI shall also work to increase the participation of underrepresented groups in mathematics through outreach to underserved high schools. The mathematical models in this project consist of ordinary differential equations (ODE) and stochastic differential equations. One of the primary goals is to build ML tools based on biophysically accurate models of neurons. These models will use the formalism developed by Hodgkin and Huxley. The key problem to be addressed here is how learning can occur with highly nonlinear models and time dependence through improvements on the backpropagation technique. Additionally, the PI will develop approaches that use predictions from currently developed models to enhance classification in ML. Key problems to address here are how to classify ODE models' simulations or incorporate uncertainty into ODE models properly. The methods will be tested against experimental data on human sleep.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.