Assessing the Reliability of Complex Models Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012) / Chapter Skim
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Advances in computing hardware and algorithms have dramatically improved the ability to computationally simulate complex processes, enabling simulation and analysis of phenomena that in the past could be addressed only by resource-intensive experimentation, if at all. Computational models are being used to study processes as large scale as the evolution of the universe and as small scale as protein folding.
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National Nuclear Security Administration, the DOE's Office of Science, and the Air Force Office of Scientific Research requested that the National Research Council study the mathematical sciences foundations of verification, validation, and uncertainty quantification (VVUQ) and recom mend steps that will lead to improvements in VVUQ capabilities.
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• Principle: The efficiency and effectiveness of validation and prediction assessments are often improved by exploiting the hierarchical composition of computational and mathematical models, with assessments beginning on the lowest-level building blocks and proceeding to successively more complex levels. -- Best practice: Identify hierarchies in computational and mathematical models, seek measured data that facilitate hierarchical validation assessments, and exploit the hierarchical composition to the extent possible.
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PROMISING RESEARCH AREAS After surveying today's VVUQ methods and their mathematical foundations, the committee identified several research topics that offer the promise of improved methods and improved outcomes. The areas identified for veri fication research are discussed in detail in Chapter 3 and summarized in Chapter 7; they include: • Development of goal-oriented a posteriori error-estimation methods that can be applied to mathematical models that are more complicated than linear elliptic partial differential equations (PDEs)
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Future advances will be determined in part by how well VVUQ methodology can integrate with the next generation of computational models, highperformance computing infrastructure, and subject-matter expertise. This integration will require that students in these various areas be adequately educated in the mathematical foundations of VVUQ.
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Finally, it has discussed changes in the education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. The committee offers its observations and recommendations in the hope that they will help the VVUQ community as it continues to improve VVUQ processes and broaden their applications.
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