Center for Computing Research (CCR)

Center for Computing Research

John Davis Jakeman

John Davis Jakeman
Optimization and Uncertainty Quantification
Email: jdjakem@sandia.gov
Phone: 505/284-9097

Mailing address:
Sandia National Laboratories
P.O. Box 5800, MS 1318
Albuquerque, NM
87185-1320
  • 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.  

 

Education/Background

  • 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

2018
  • Adcock, Ben, Anyi Bao, John Davis Jakeman, Akil Narayan, "Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations," Journal Article, SIAM/ASA Journal on Uncertainty Quantification (JUQ), Submitted January 2018.
  • Butler, Troy, John Davis Jakeman, Timothy Michael Wildey, "Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems," Journal Article, SIAM Journal on Scientific Computing, Accepted/Published April 2018.
  • Gorodetsky, Alex, John Davis Jakeman, "Gradient-based Optimization for Regression in the Functional Tensor-Train Format," Journal Article, Journal of Computational Physics, Submitted January 2018.
  • Jakeman, John Davis, Akil Narayan, "Generation and application of multivariate polynomial quadrature rules," Journal Article, Computer Methods in Applied Mechanics and Engineering, Accepted/Published April 2018.
2017
  • Jakeman, John Davis, Akil Narayan, Tao Zhou, "A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions," Journal Article, SIAM Journal on Scientific Computing, Accepted/Published January 2017.
  • Narayan, Akil, John Davis Jakeman, Tao Zhou, "A Christoffel function weighted least squares algorithm for collocation approximations," Journal Article, Mathematics of Computation, Vol. 86, pp. 1913–1947 , Accepted/Published January 2017.
2015
2014
2013
  • Jakeman, John D., Akil Narayan, Dongbin Xiu, "Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions," Journal Article, Journal of Computational Physics, Vol. 242, No. 1, pp. 790–808, Accepted/Published June 2013.
2010