Research Interests

  • Uncertainty quantification and stochastic modeling
  • Numerical analysis and high-performance scientific computing
  • Data-driven and reduced-order modeling
  • Mori-Zwanzig formulation
  • Numerical approximation of functional differential equations
  • Theoretical and computational fluid dynamics

Determining the statistical properties of nonlinear dynamical systems is a problem of major interest in many areas of science and engineering. Even with recent theoretical and computational advancements, no broadly applicable technique has yet been developed for dealing with the challenging problems of high dimensionality, model uncertainty, multi-scale features and random frequencies. 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 numerical 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/

Numerical 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 SciencesPhysics Reports)

Appointments

  • 2021 - present, Professor of Applied Mathematics, UC Santa Cruz.
  • 2019 - 2021, Associate Professor of Applied Mathematics, UC Santa Cruz.
  • 2015 - 2019, Assistant Professor of Applied Mathematics, UC Santa Cruz.
  • 2010 - 2015, Research Assistant Professor of Applied Mathematics, Brown University.
  • 2006 - 2010, Postdoctoral Research Associate at the Department of Energy, Nuclear and Environmental Engineering, University of Bologna.