The non-Abelian X-ray transform
The link for participation in the event is the following: https://fernuni.zoom.us/j/64850280617.
Thursday, November 18, 2021
5 p.m., on Zoom
This work introduces a method for learning low-dimensional dynamical-system models from data of high-dimensional black-box systems. The key contribution is a data sampling scheme that introduces a re-projection step to obtain trajectories corresponding to Markovian dynamics in low-dimensional subspaces. Models fitted to re-projected trajectories exactly match reduced models that are traditionally constructed with model reduction techniques from full knowledge of the governing equations and their discrete operators of the high-dimensional systems. Building on a posteriori error estimators from traditional model reduction, we derive probabilistic bounds for the generalization error of the models learned from data. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions for establishing trust in decisions made from data.
Benjamin Peherstorfer is Assistant Professor at Courant Institute of Mathematical Sciences. His research focuses on computational methods for data- and compute-intensive science and engineering applications, including scientific machine learning, mathematics of data science, model reduction, and computational statistics.