Computational Filtering Methods for Time-Varying Parameter Estimation in Nonlinear Systems

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Many applications in modern science involve unknown system parameters that must be estimated using little to no prior information. In mathematical models to analyze and predict the behavior of such systems, the problem of estimating and quantifying uncertainty in model parameters remains a challenge. This is particularly true for systems where knowledge of parameter values is critical in obtaining trustworthy model output, as in patient-specific models for personalized medicine, for example. A subset of these problems includes parameters of the type that are known to vary with time but do not have known evolution models. Examples include the seasonal transmission parameter in modeling the spread of infectious diseases and the external voltage parameter in modeling the spiking dynamics of neurons. In certain cases, the parameters may have some known structural characteristics (such as periodicity) that can be utilized in and maintained throughout the estimation process. However, the main challenge in estimating time-varying parameters lies in accurately accounting for their time evolution without detailed information regarding their temporal dynamics. The goal of this project is to design and analyze novel computational methods for estimating such time-varying parameters.The aim of this study is to design and analyze novel computational methods for estimating time-varying parameters through use of nonlinear filtering. Leveraging the strengths of the Bayesian statistical filtering framework, where prior beliefs are naturally incorporated, this work will involve developing models for parameter evolution that take into account prior knowledge relating to the structure or behavior of the parameter over time without defining explicit functions to describe the dynamics. Methods will also be developed for more difficult problems where there may not be any parameter structural characteristics known a priori. The algorithms and computational tools developed in this study will be applied to data for a variety of nonlinear systems, which may further inspire new directions for methodological advancement. Specific areas of application include engineering and the life sciences, with particular application to surgical robotics involving tissue thermal response to laser-based microsurgery.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.