Collaborative Research: Efficient Methods for Identifiability of Dynamic Models

该项目的目标是分析和改进生物学和其他科学研究人员开发的动态模型的校准，以模拟真实世界的过程。数学模型在生物学中被广泛用于理解机制，进行预测和指导干预策略。为此，模型参数通常必须使用数据进行校准;估计的参数可能对从模型和数据生成的见解的可靠性具有重要意义。这就提出了一个重要的问题，即校准过程是否是适定性的，即是否有可能从给定类型或数据集中唯一地估计模型参数？可识别性分析是对这些问题的研究，该项目将改进和扩展目前可用的代数可识别性方法集，使其建立在更坚实的理论基础上，并解决在许多生物环境中广泛使用的新型模型。在学术界之外，即将开发的算法将使研究人员能够成功地将模型和实验联系起来，以生成基于模型的见解，从而改善现实世界的治疗策略。将向两名博士提供培训。为这个项目做研究的学生。培训部分还将包括跨学科课程开发以及一个包含辅导讲座和问题会议的会议，以教育该项目中开发的理论，算法和软件的工业和学术参与者。 本项目由数学科学部数学生物学和计算与通信基金会数学基金会项目部共同资助，具体而言，研究人员将开发、分析和实现符号和符号-数值算法，对生物学和其他科学中出现的动态模型（包括常微分（ODE）、延迟和差分方程模型）进行可识别性分析。使用这些算法，他们还将对从细胞信号传导和生理学应用中提取的一系列模型进行可识别性分析。所提出的算法将基于微分-差分代数，其通过对模型方程应用微分-差分消除算法来连接到有理ODE/延迟/差分方程的常见情况下的可识别性。这样的符号方法已被证明是生产领域的参数识别。所提出的方法将允许分析一大类模型的结构可识别性，允许人们评估哪些参数可以估计和定制实验设计，以回答感兴趣的问题，治疗策略和机制的见解。对于第一次，严格的理由和分析有效的算法将可用于识别问题的延迟和差分方程模型。证明和更有效的算法将出现在ODE模型的全局可识别性问题。为了开展拟议的研究，微分/差分方程的代数理论将取得新的进展。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

The goal of the project is to analyze and improve the calibration of dynamic models developed by researchers in biology and other sciences to model real-world processes. Mathematical models are used broadly across biology to understand mechanisms, make predictions, and guide intervention strategies. To do so, the model parameters often must be calibrated using data; the estimated parameters can have significant implications for reliability of insights generated from the model and data. This raises the important question of whether the calibration process is well posed, i.e. is it possible to uniquely estimate model parameters from a given type or set of data? Identifiability analysis is the study of these issues, and this project will improve and expand the currently available set of algebraic identifiability methods to set them on a firmer theoretical basis and address new types of models used broadly in many biological settings. Beyond academia, the algorithms to be developed will allow researchers to successfully link models and experiments to generate model-based insights that improve real-world treatment strategies. Training will be provided to two Ph.D. students working on research for this project. The training component will also include interdisciplinary course development as well as a conference with tutorial lectures and problem sessions to educate industrial and academic participants in the theory, algorithms, and software developed in this project. This project is supported jointly by the Division of Mathematical Sciences Mathematical Biology and Division of Computing and Communication Foundations Algorithmic Foundations programs.More specifically, the investigators will develop, analyze, and implement symbolic and symbolic-numeric algorithms that perform identifiability analysis of dynamic models (including ordinary differential (ODE), delay, and difference equation models) that appear in biology and other sciences. Using these algorithms, they will also carry out identifiability analysis for a range of models drawn from cellular signaling and physiology applications. The proposed algorithms will be based on differential-difference algebra, which connects to identifiability in the common case of rational ODEs/delay/difference equations by applying differential-difference elimination algorithms to the model equations. Such symbolic methods for ODE models have proven to be productive in the area of parameter identifiability. The proposed methods would allow a large class of models to be analyzed for structural identifiability, allowing one to assess which parameters can be estimated and tailor experiment design to answer the questions of interest for treatment strategies and mechanistic insights. For the first time, rigorously justified and analyzed efficient algorithms will be available for identifiability problems in delay and difference equation models. Certified and more efficient algorithms will appear for global identifiability problems in ODE models. To carry out the proposed research, new advances in the algebraic theory of differential/difference equations will be made.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.