Andrea Arnold, assistant professor of mathematical sciences, has receives a three-year, $220,458 award from the National Science Foundation for a project titled, “Computational Filtering Methods for Time-Varying Parameter Estimation in Nonlinear Systems. ” The aim of the study is to design and analyze novel computational methods for estimating time-varying parameters through use of nonlinear filtering. The research has applications in the life sciences, such as modeling the spread of infectious diseases, determining the optimal treatment strategy for HIV drug therapy, and modeling tissue response to laser-based microsurgery.
Arnold’s research in applied mathematics focuses on inverse problems and uncertainty quantification, which involves estimating unknown system parameters using indirect observations and analyzing the changes in predicted outcomes due to changes in the inputs. Many applications in modern science involve system parameters that are estimated using little prior information. This poses a challenge in applied and computational mathematics, particularly for problems where knowledge of parameters is crucial in obtaining trustworthy model output.
The study will develop mathematically sound and computationally efficient systematic approaches for estimating time-varying parameters with unknown dynamics. This work also will involve developing models for parameter evolution that take into account any prior knowledge relating to the structure or behavior of the parameter over time without defining explicit functions to describe the dynamics. Arnold will include WPI undergraduates and graduate students on the project team starting in the summer of 2019.