Research Interests
My research activity has been recently focused on developing new theoretical and computational methods for uncertainty quantification and dimensional reduction in large scale stochastic dynamical systems. In particular, I have been working on the Mori-Zwanzig formulation, data-driven modeling, hierarchical tensor methods for the numerical solution to high-dimensional PDEs, and the approximation of functional differential equations (e.g., Hopf characteristic functional equations).
My research featured in the UCSC magazine Inquiry : https://inquiry.ucsc.edu/2020-21/superior-simulations/
Approximation of Functional Differential Equations: https://www.soe.ucsc.edu/news/prof-venturi-addresses-long-standing-open-problem-computational-mathematics (PAPERS: Research in the Mathematical Sciences, Physics Reports)
Appointments