On Low-Rank Regularization for Ill-Posed Nonlinear Parameter Estimation

病态非线性参数估计的低秩正则化

• 批准号: 2011622
• 负责人: Alexandra Smirnova
• 金额: $ 20万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2011622&HistoricalAwards=false
• 关键词: Low; Rank; Regularization; Ill; Posed

This research has been inspired by numerous challenges in studying the transmission dynamics of infectious diseases. The investigator will focus on estimating parameters of data-enabled mathematical models of infectious disease aiming to generate forecasts of future incidence cases. The project will develop regularized computational algorithms for this data estimation which presents many challenges and includes uncertainties. The models and optimization methods to be used are important in anticipating the resources needed for disease management. Data on past and present infectious diseases will be studied, and the investigator will collaborate with the university's School of Public Health. Apart from applications in epidemiology, this project will have a broad impact on scientific disciplines including signal and image processing, biomedical imaging, gravitational sounding, chaos theory, ocean acoustics, and others. The project includes graduate student training through involvement in the research.The project aims to develop computational algorithms for estimating parameters using optimization. From an optimization standpoint, parameter estimation and forecasting from data comes down to solving an ill-posed minimization problem constrained by a system of ordinary or partial differential equations. For uncertainty quantification, multiple runs of the inversion algorithm must be carried out, preferably in real time. To address this challenge, the project will construct a family of trust-region optimization algorithms with low-rank updates for the Jacobian operator that will reduce the computational cost of a quasi-Newton step and, at the same time, incorporate an extra layer of stability in the iterative process. In case of nonlinear least squares with non-zero residuals, low-rank updates for stable Hessian evaluation will be investigated. Theoretical and numerical analysis of the new methods will be first carried out for normally solvable ill-posed operator equations and then extended to essentially ill-posed problems. The successful completion of this project will advance the understanding of ill-posed inverse problems and facilitate more stable and efficient simulations.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.

这项研究受到了研究传染病传播动力学的众多挑战的启发。研究人员将专注于估计传染病数据支持数学模型的参数，旨在预测未来的发病率。该项目将为这种数据估计开发正则化计算算法，这带来了许多挑战，包括不确定性。所使用的模型和优化方法对于预测疾病管理所需的资源非常重要。将研究过去和现在的传染病数据，研究人员将与该大学的公共卫生学院合作。除了在流行病学中的应用外，该项目还将对包括信号和图像处理、生物医学成像、重力探测、混沌理论、海洋声学等在内的科学学科产生广泛的影响。该项目包括通过参与研究对研究生进行培训。该项目旨在开发使用优化估计参数的计算算法。从优化的角度来看，参数估计和预测数据归结为解决一个不适定的最小化问题的约束下的一个系统的常微分方程或偏微分方程。对于不确定性量化，必须执行反演算法的多次运行，优选地以真实的时间进行。为了应对这一挑战，该项目将构建一系列具有Jacobian算子低秩更新的信赖域优化算法，这将降低拟牛顿步骤的计算成本，同时在迭代过程中加入额外的稳定层。在具有非零残差的非线性最小二乘的情况下，将研究稳定Hessian评估的低秩更新。理论和数值分析的新方法将首先进行正常可解不适定算子方程，然后扩展到本质上不适定的问题。该项目的成功完成将促进对不适定逆问题的理解，并促进更稳定和更有效的模拟。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智力价值和更广泛的影响审查标准进行评估来支持。

项目成果

On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission

具有量化不确定性的稳定参数估​​计和短期预测及其在 COVID-19 传播中的应用

• DOI: 10.1515/jiip-2021-0037
• 发表时间: 2022
• 期刊: Journal of Inverse and Ill-posed Problems
• 影响因子: 1.1
• 作者: Smirnova, Alexandra;Pidgeon, Brian;Luo, Ruiyan
• 通讯作者: Luo, Ruiyan

The doubling time analysis for modified infectious disease Richards model with applications to COVID-19 pandemic

• DOI: 10.3934/mbe.2022150
• 发表时间: 2022-01-01
• 期刊: MATHEMATICAL BIOSCIENCES AND ENGINEERING
• 影响因子: 2.6
• 作者: Smirnova, Alexandra;Pidgeon, Brian;Zhao, Yichuan
• 通讯作者: Zhao, Yichuan

Mathematical and Statistical Analysis of Doubling Times to Investigate the Early Spread of Epidemics: Application to the COVID-19 Pandemic

• DOI: 10.3390/math9060625
• 发表时间: 2021-03-01
• 期刊: MATHEMATICS
• 影响因子: 2.4
• 作者: Smirnova, Alexandra;DeCamp, Linda;Chowell, Gerardo
• 通讯作者: Chowell, Gerardo