Computational Framework for Extreme System Responses
A Warren Distinguished Lecture with
Mircea Grigoriu
Civil and Environmental Engineering
Center for Applied Mathematics
Cornell University
ABSTRACT
In this talk, Mircea Grigoriu develops a practical method for estimating the distribution of extreme solutions of stochastic problems. The first part of the presentation reviews essential concepts of probability theory and illustrates the need for uncertainty quantification in engineering via simple examples. The second part presents the computational framework for estimating extremes of random processes. Since these functions are uncountable families of random variables and numerical methods can solve stochastic problems involving finite sets of random variables, only extremes of finite dimensional (FD) surrogates, i.e., deterministic functions of time and finite sets of random variables, of target processes can be characterized numerically. Grigoriu establishes conditions under which the distributions of extremes of FD models can be used as approximations for those of target processes. The implementation and accuracy of the method are illustrated by numerical examples from dynamics and material science.
SPEAKER
Mircea Grigoriu holds degrees in Structural Engineering (Bucharest Institute of Civil Engineering), Mathematics (University of Bucharest), and a Ph.D. in Civil Engineering from MIT. He has authored over 200 technical papers and six books Random Vibration of Mechanical and Structural Systems (with T.T. Soong, Prentice Hall, 1992), Applied Non-Gaussian Processes (Prentice Hall, 1995), Stochastic Calculus, Applications in Science and Engineering (Birkhuaser, 2002), Stochastic Systems: Uncertainty Quantification and Propagation (Springer, 2012), Linear Dynamical Systems (Springer, 2021), and Numerical Methods for Extreme Responses of Dynamical Systems (Springer, 2025).
Grigoriu has received the 1993 IASSAR Research Prize, the 1998 SAE Distinguished Probabilistic Methods Education Award, the election to the Romanian Academy of Technical Sciences (2004), the 2002 Alfred Freudenthal Medal, the Daniel M. Lazar’29 Excellence in Teaching Award (2003), the title of Doctor Honoris Causa, Technical University of Civil Engineering, Bucharest, Romania (2004), the 2005 Norman Medal of ASCE, the grade of EMI Fellow, 2014, and the 2016 Newmark Medal. Also, he is on the editorial board of numerous technical journals.
