Campus Directory

Division Baskin School of Engineering

Department/College/Unit Applied Mathematics

Title Professor

Affiliation Faculty

Other UCSC Campus Affiliation Mathematics Department

Faculty Type Regular Faculty

Areas of Expertise Mathematical Modeling
Applied Physics
Fluid Dynamics
Statistics
Mathematics
Machine Learning
Physics
Supercomputing

Web Site

Primary Office Location Jack Baskin Engineering Building
BE 361C

Additional Location(s) Baskin Engineering, Room 353B

Mail Stop SOE2

Research Interests

• Uncertainty Quantification (UQ) and computational probability
• Multi-fidelity stochastic modeling and data-driven stochastic multiscale mathematics
• Numerical analysis and high-performance scientific computing
• Probability density function methods for forward and inverse UQ problems
• Mori-Zwanzig approach to dimension reduction and uncertainty quantification
• Functional differential equations

Selected Publications

P. Perdikaris, D. Venturi, J. O. Royset, G. E. Karniadakis, ``Multi-fidelity modeling via recursive co-kriging and Gaussian Markov random fields'', Proc. R. Soc. A, 2015, 471, pp. 2179(1-20) PDF

D. Venturi and G. E. Karniadakis, ``Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems'', Proc. R. Soc. A, 2014, 470, pp. 2166(1-20) PDF

H. Cho, D. Venturi and G. E. Karniadakis, ``Statistical analysis and simulation of random shocks in stochastic Burgers equation'', Proc. R. Soc. A, 2014, 470, pp. 2171(1-21) PDF

D. Venturi, ``Conjugate flow action functionals'', J. Math. Phys., 2013, 54, pp. 113502(1-19) PDF

H. Cho, D. Venturi and G. E. Karniadakis, ``Karhunen-Loève expansion for multiple correlated stochastic processes'', Prob. Eng. Mech., 2013, 34, pp. 157-167 PDF

D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovskii and G. E. Karniadakis, ``Wick-Malliavin approximation to nonlinear stochastic PDEs: Analysis and Simulation'', Proc. R. Soc. A, 2013, 469, pp. 2158(1-20) PDF

H. Cho, D. Venturi and G. E. Karniadakis, ``Adaptive discontinuous Galerkin method for response-excitation PDF equations'', SIAM J. Sci. Comput., 2013, 35(4), pp. B890-B911 PDF

D. Venturi, T. P. Sapsis, H. Cho and G. E. Karniadakis, ``A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems'', Proc. R. Soc. A, 2011, 468, pp. 759-783 PDF

D. Venturi, ``On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate'', J. Fluid Mech., 2006, 559, pp. 215-254 PDF

D. Venturi, X. Wan and G. E. Karniadakis, ``Stochastic bifurcation analysis of Rayleigh-Bénard convection'', J. Fluid Mech., 2010, 650, pp. 391-413 PDF