Senior Scientist, Professor & Department Head

CLAYTON G. WEBSTER, Ph.D.

Research interests

My research is focused on mathematical rigor but is interdisciplinary in nature, combining numerical and functional analysis, approximation theory, statistics, as well as scientific computing. My expertise is in the development, approximation, and analysis of computational techniques for optimal recovery of an underlying high-dimensional function, having a certain set of constraints, from a limited number of simulations or measurements.

The types of high-dimensional functions that I am particularly interested in are found in many fields. Examples include uncertainty quantification, optimal control, and parameter identification for complex systems, kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, Fokker-Planck and fluid dynamics equations for complex fluids, turbulent flow, quantum dynamics, molecular life sciences, as well as nonlocal mechanics.

These high-dimensional phenomena, in turn, are typically models described by (partial-integro) differential equations, consisting of many spatial, phase, and stochastic variables, defined over a multidimensional domain whose dimension can be very large, or even infinite. The physical and phase parameters naturally arise in the deterministic and probabilistic description of complex physical, social, and financial processes including particle transport, multi-phase flow, chemical reaction and biological networks, non-Newtonian fluids, as well as quantum chemistry and mechanics. On the other hand, stochastic parameterizations are employed to quantitatively characterize uncertainty in the input data (coefficients, forcing terms, boundary conditions, geometry, etc.). Examples include both epistemic (lack of knowledge) and aleatoric (intrinsic variability) and encompass uncertainty coming from inaccurate physical measurements, bias in mathematical descriptions as well as errors coming from computational simulations.

These types of uncertainties are inescapable in the the majority of large-scale applications,

including the enhancement and reliability of smart energy grids, development of renewable energy technologies, vulnerability analysis of water and power supplies, climate change estimation, accelerating the design and discovery of new materials, and cost-effective designs of current and future nuclear reactors.

The goal of the computational simulation is to guarantee the simultaneous reconstruction of the entire high-dimensional solution map up to a prescribed accuracy, with minimal computational cost. Unfortunately, the computational effort of most approaches explodes as the dimension increases; well beyond the capacity of the largest advanced computer architecture for the foreseeable future. Therefore, simulating the entire system at the level of fidelity that truly predicts the solution as a function of the high-dimensional parametrization, remains elusive outside of idealized situations. As a consequence, the goal of my research and my mathematical expertise, in large part, lies in numerical analysis and approximation theory with particular focus on the development of:

- adaptive sparse polynomial approximation techniques such as interpolation, projection, and compressed sensing, as well as nonlinear approximations that exploit smoothness, weighted sparsity, and compression, to overcome the curse of dimensionality;

- continuous, semi-discrete and fully- discrete space-time discretizations of deterministic and stochastic partial differential equations;
- convergence, error estimates, explicit cost bounds and complexity analysis, as well as stable and accurate numerical algorithms;
- approximating deterministic and stochastic inverse problems, optimal control, and parameter estimation;
- rigorous analysis and algorithm development for nonlocal mechanicals and multiscale/multiphysics processes;
- image compression and optimal function recovery from limited measured data, and;
- mathematics of finance, data-driven modeling, and time-series analysis.

With the goal of approaching such problems with mathematical rigor while focusing of large-scale applications, I utilize a broad array of theoretical and computational tools, including:

measure and integration theory, probability and random matrix theory, statistics, Ito calculus,

Fourier analysis, adjoint based methods, calculus of variations, semigroup theory, collocation methods, sparse grid quadrature and interpolation, functional, convex and multi-resolution analysis, adaptive high-order spectral approximations, model reduction, linear and nonlinear filtering, as well as homogenization.

Several of my funded research projects aim at establishing a modern mathematical and statistical foundation that will enable next-generation, complex, stochastic predictive simulations. Such a foundation is critical to realizing the potential of future computing platforms, including exascale, and will ultimately empower scientists to address a fundamental question, namely "how do the uncertainties ubiquitous in all modeling efforts affect our predictions and understanding of complex phenomena?" Our collaborative approach to uncertainty quantification (UQ) combines novel paradigms in applied mathematics, statistics and computational science into a rigorous mathematical methodology, which we call the Environment for Quantifying Uncertainty: Integrated aNd Optimized at the eXtreme-scale (EQUINOX), as well as an unified computational framework, entitled the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (TASMANIAN). A complete summary of my current and previously funded research projects can be found here.

In addition, a listing of my publications and most recent ORNL reports can be found here.

Finally, you can download a copy of my CV below.

Latest news

July, 2015:

Drs. Clayton Webster and Guannan Zhang, together with Profs. Wolfgang Dahmen (RWTH Aachen), Ron DeVore (TAMU), Qiang Du, Max Gunzbugrer (FSU), and Nicholas Zabaras (Warwick) awarded $3.5M by the DOD (DARPA) for the project FORMULATE.

June, 2015:

Profs. Qiang Du, Steve Hou, Pavel Bochev, and Clayton Webster named Guest Editors for the Special Issue

of Computer & Mathematics with Applications, honoring the 70th birthday of Prof. Max Gunzburger.

May, 2015:

Congratulations to Prof. Max Gunzburger, who was awarded the prestigious Lawton Distinguish Professor.

April, 2015:

Co-organizers Profs. Qiang Du, Steve Hou, Pavel Bochev, and Clayton Webster announced that the Workshop on Advances in Scientific Computing and Applied Mathematics (ASCAM15) will be held at the Stratosphere Hotel in Las Vegas, NV, October 9-12.

March, 2015:

Profs. Peter Binev Wolfgang Dahmen, Ron DeVore, and Max Gunzburger visited Dr. Webster March 8-12.

January, 2015:

Dr. Duncan and Dr. Webster welcome their beautiful angel, Quinn Elise Webster on January 25th, 2015!!!

December, 2014:

Dr. Webster was elected as Program Director of the SIAM Activity Group on Uncertainty Quantification.

November, 2014:

Magazine article "Computational tool lowers cost, improves exploration accuracy," describes our latest work.

November, 2014:

Profs. Jim Berger, Fabio Nobile and Clayton Webster were named Co-Chairs of the SIAM UQ16 Conference.

October, 2014:

Drs. Archibald (PI) and Webster (co-PI) were awarded $2M by the DOE (ASCR) for the project entitled ACUMEN.

Upcoming talks & travel

May, 2015: IAS, Munich Germany

Dr. Webster will present an invited talk in the symposium on "Big Data and Predictive Computational Modeling,"

at the Institute for Advanced Study, Technical University of Munich.

June, 2015: Paris VI, Paris, France

Dr. Webster will visit Profs. Albert Cohen and Ron DeVore and give an invited talk in the Department of Mathematics, Université Pierre et Marie Curie.

July, 2015: USNCCM13, San Diego

Dr. Webster will present an invited talk at the USACM's 13th U.S. National Congress for Computational Mechanics.

August, 2015: ICIAM 2015, Beijing, China

Dr. Webster will attend part of the ICIAM 2015 meeting and and present an invited talk.

August, 2015: AFOSR Math Review, Washington, DC

Dr. Webster will present an invited talk at the AFOSR Computational Math Annual PI Meeting.

August, 2015: Jeju Island, South Korea

Dr. Webster will present an invited talk at the workshop on "Computational Mathematics and Scientific Computing," in honor of Prof. Gunzburger's 70th birthday.

September, 2015: The 6th HDA, Bonn, Germany

Dr. Webster will present an invited talk at the 6th workshop on "High-Dimensional Approximation," at

the University of Bonn.

September, 2015: ASCAM15, Las Vegas, NV

Dr. Webster is a co-organizer of the ASCAM15 workskop and will present an invited talk.

December 2015: BIRS Workshop, Banff, Canada

Dr. Webster will attend and speak at Banff International Research Station workshop entitled "Approximation of high-dimensional numerical problems."

April, 2016: SIAM UQ16, Lusanne, Switzerland

Dr. Webster is Co-Chairing the SIAM Conference of UQ and will present several invited talks.

May, 2016: VIU, San Servolo Island, Venice, Italy

Dr. Webster is giving an invited talk at the "Challenges in high dimensional analysis and computation."

DOWNLOAD COMPLETE CV

updated: 08/2015

Contact information

Computational & Applied Mathematics

Oak Ridge National Lab

One Bethel Valley Road

P.O. Box 2008, MS-6164

Oak Ridge, TN 37831-6164

Department of Mathematics

The University of Tennessee

227 Ayres Hall

1403 Circle Drive

Knoxville, TN 37996-1320

email: webstercg@ornl.gov

phone: 865-574-3649

google: 609-379-3271

fax: 865-241-5552

Administrative Assistant

Ms. Nancy Valentine

865-241-0212

Clayton G. Webster, 2015