Uncertainty Quantification for Systems Governed by Partial Differential Equations. Workshop report

Abstract

In deterministic mathematical modeling, complete knowledge of input parameters is assumed. This leads to simplified, tractable computations and produces simulations of outputs that correspond to specific choices of inputs. However, most physical, biological, social, economic and financial processes involve some degree of uncertainty. Uncertainty quantification (UQ) is the task of determining statistical information about the outputs of a process of interest, given only statistical (i.e. incomplete) information about the inputs. It encompasses many tasks that are crucial to both public and private enterprise. This includes, crucially, risk assessments that are typically used to inform policy makers e.g. on sensitive issues such as the safety of a nuclear waste repository. It has long been recognized that mathematical models need to account for uncertainty but progress has been hampered by a lack of mathematical analysis and computing resources. The science of UQ has been in its infancy in many application areas until relatively recently but is now rapidly developing. The workshop brought together numerical analysts, probabilists, computer scientists and industrialists (amongst whom there is traditionally very little communication) to disseminate important advances currently being made in sparse high-dimensional sampling, high-dimensional quadrature, approximation theory, model-order reduction, sensitivity analysis, statistics and scientific computing.

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Document Details

Document Type
Technical Report
Publication Date
Jun 12, 2012
Accession Number
ADA562693

Entities

People

  • Andrew Cliffe
  • Catherine Powell
  • Max Gunzburger
  • Paul Houston

Organizations

  • Heriot-Watt University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematical Models
  • Models
  • Nuclear Materials
  • Numerical Analysis
  • Risk Analysis
  • Sampling
  • Scientists
  • Sensitivity
  • Simulations
  • Statistics
  • Uncertainty
  • Workshops

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Economics
  • Systems Analysis and Design