Faculty & Staff Directory
- Assistant Professor
PhD, Mathematical Sciences, George Mason University, (2013).
My research is motivated by the rapid expansion of model complexity and data availability in the applied sciences. Traditional parametric modeling is subject to model error and I believe that modern complex systems call for model-free and semi-parametric approaches. In order to avoid the curse-of-dimensionality, these approaches must effectively incorporate available prior knowledge and existing models. My goal is to develop these techniques with careful consideration of the goals and constraints of real world case studies. I collaborate across disciplines and with graduate students and advanced undergraduate students to advance this research and train new researchers.
- Geometry of data: diffusion maps/local kernels, nonlinear dimensionality reduction and decomposition
- Statistics: kernel density/operator estimation, semi-parametric modeling of dynamical systems
- Dynamical systems: data assimilation, prediction/control, and uncertainty quantification
- Harmonic analysis: Sampling theory on manifolds, connections to kernel based statistical estimates
My goal in teaching is to reach every student and communicate both the how and the why of the mathematical methods under consideration. I hope to excite students' latent curiosity with guided projects allowing space for self-discovery while still giving guiding structure through traditional lectures and clear expectations. Recent courses include Mathematics of Manifold Learning, Advanced Calculus, and Numerical Analysis.
- T. Berry, T. Sauer, Local Kernels and the Geometric Structure of Data. Journal of Applied and Computational Harmonic Analysis, 2015.
- T. Berry, J. Harlim, Variable Bandwidth Diffusion Kernels. Journal of Applied and Computational Harmonic Analysis, 2015.
- T. Berry, D. Giannakis, J. Harlim, Nonparametric forecasting of low-dimensional dynamical systems. Physical Review E, 2015.
- T. Berry, R. Cressman, Z. Greguric-Ferencek, T. Sauer, Time-scale separation from diffusion-mapped delay coordinates. SIAM J. Appl. Dyn. Sys., 2013.
- T. Berry, T. Sauer, Adaptive ensemble Kalman filtering of nonlinear systems. Tellus A, 2013.
The Diffusion Forecast
The Diffusion Forecast is a model-free method of forecasting based on time series data.