Research InterestsScientific computing
CoursesI will be teaching Section 002 of Math 5651 in Spring 2014.
Here is the homepage for the course.
FundingCollaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)
PublicationsPreprints for most of the publications can be found on the Arxiv
Preprints:P. S., Model reduction and mesh refinement (2014), arXiv:1402.6402v1.
J. Li, P. S., Mesh refinement for uncertainty quantification through model reduction (2014), arXiv:1402.4877v1.
P. S., Mori-Zwanzig reduced models for uncertainty quantification II: Initial condition uncertainty (2012), arXiv:1212.6360v1.
P. S., Mori-Zwanzig reduced models for uncertainty quantification I: Parametric uncertainty, (2012), arXiv:1211.4285v1.
Journal publications:P. S., Renormalized reduced models for singular PDEs, Communications in Applied Mathematics and Computational Science Vol. 8 (2013), No. 1, pp. 39-66.
P. S., Numerical computation of solutions of the critical nonlinear Schr\"odinger equation after the singularity, Multiscale Modeling and Simulation 10 (2012), pp. 48-60.
P. S., Stochastic global optimization as a filtering problem, Journal of Computational Physics 231 (2012), pp. 2002-2014.
V. Maroulas and P. S., Improved particle filters for multi-target tracking, Journal of Computational Physics 231 (2012), pp. 602-611.
P. S., Conditional path sampling of stochastic differential equations by drift relaxation, Communications in Applied Mathematics and Computational Science (2011) Vol. 6, No 1, pp. 63-78.
P. S., A phase transition approach to detecting singularities of partial differential equations, Communications in Applied Mathematics and Computational Science Vol. 4 (2009), No. 1, 217-239.
D. Givon, P. S. and J. Weare, Dimensional reduction for particle filters of systems with time-scale separation, IEEE Transactions on Signal Processing Vol.57 No.2 (2009) pp. 424-435.
O.H. Hald, P. S., Optimal prediction and the rate of decay for solutions of the Euler equations in two and three dimensions, Proceedings of the National Academy of Sciences 104, no 16, (2007) pp. 6527-6532 (Published with a Commentary, same issue of PNAS, pp. 6495-6499)
P. S., Higher order Mori-Zwanzig models for the Euler equations, Multiscale Modeling and Simulation 6, no 3, (2007) pp. 741-760.
P. S., A comparative study of two stochastic mode reduction methods Physica D 213 (2006) pp. 197-213.
A.J. Chorin, P. S., Problem reduction, renormalization and memory, Communications in Applied Mathematics and Computational Science 1 (2005) pp. 1-27.
P. S., A maximum likelihood algorithm for the estimation and renormalization of exponential densities, Journal of Computational Physics 208 (2005) pp. 691-703.
P. S., Stochastic optimal prediction for the Kuramoto-Sivashinsky equation, Multiscale Modeling and Simulation 2, no 4, (2004) pp. 580-612.
P. S., A hybrid method for the inviscid Burgers equation, Discrete and Continuous Dynamical Systems 9 (2003) pp. 793-799.
Technical Reports & theses:P. S., Dimensional reduction approach to shock capturing, Technical Report - Center for Turbulence Research, Stanford (2008).
P. S., Dimensional reduction as a tool for mesh refinement and tracking singularities of PDEs, Technical Report LBNL-62851 (2007).
P. S., A.J. Chorin, Numerical scaling analysis of the small-scale structure in turbulence, Technical Report LBNL-59490 (2006).
P. S., Stochastic Optimal Prediction for the Kuramoto-Sivashinsky Equation, PhD Thesis, Columbia University, New York, October 2003.