Center for Computing Research
John Davis Jakeman
|John Davis Jakeman|
Optimization and Uncertainty Quantification
Sandia National Laboratories
P.O. Box 5800, MS 1318
- Spectral stochastic expansions: I have extensive experience developing and applying Polynomial Chaos Expansions (PCE) for quantifying uncertainty. Recently I have combined iterative basis selection with compressed sensing to efficiently estimate PCE coefficients from structured and unstructured data. I have also developed locally and dimension adaptive sparse grid methods to construct high-dimensional surrogate models of expensive simulation models. Additional experience related to surrogate methods includes Gaussian process emulation, discontinuity detection, gradient enhanced approximations and optimal experimental design using Leja sequences.
- A posterori error analysis for finite elements and stochastic expansions: I have significant experience in numerical methods for Partial Differential Equations (PDE) including finite element and finite volume methods. I have contributed to the open source software project ANUGA which is a finite volume code that solves the shallow-water wave equations and is used to model tsunami and storm surges. I have also used finite elements in conjunction with polynomial chaos expansions, domain decomposition and dimension reduction to eficiently solve stochastic PDEs.
- Optimization and inverse problems: I am interested in inferring random fields from (possibly limited) observational data. I have applied deterministic optimization and Bayesian inference to an ice-sheet model to develop initial conditions that can be used with various climate change scenarios to predict sea level rise due to ice-sheet melt. Important aspects of this problem include using Bayesian inference for extremely high-dimensional (> 100, 000) random field parameterizations and lower-dimensional random field modeling using Karhunen Loe´ve Expansions (KLE).
- Deployment of software for uncertainty quantification: The complexity of methods used for uncertainty quantification ranges from those that are simple to code and use to those that are difficult to understand and apply. I am involved in a large team effort to build and deploy usable software tools for uncertainty quantification. The software is released in a C++ object oriented package called Dakota that aims to lessen the diffculty of applying UQ methods to real problems.
- B.Sc. Mathematics. (Honours 1). Australian National University, 2003-2006.
- Ph.D. Mathematics. Australian National University, 2007-2011.
- Postdoctoral associate. Purdue University, 2011.
- Postdoctoral associate. Statistical and Applied Mathematical Sciences Institute (SAMSI), 2011.
- Postdoctoral associate. Sandia National Laboratories, 2012-
Selected Publications & Presentations