The proposed workshop will bring together participants from applied mathematics and a wide range of computational science disciplines, mostly concerned with the solution of nonlinear partial differential equations (PDEs), for the purpose of sharing their expertise, techniques, and problematical issues with participants of similar basic interest but differing application areas. Five keynote speakers from diverse disciplines have accepted invitations to speak, with application fields of bioengineering, autonomous vehicle dynamics, computational mechanics, aerodynamics, and physics. Specific areas where applied mathematics plays a strong role will be elicited, including multiscale and multiphysics problems, single-grid error estimators with practical metrics for nonlinear problems and uncertainty quantification. Participation by applied mathematicians, graduate students, post-doctoral researchers, young faculty, and under-represented groups will be encouraged through the application of NSF funds towards travel grants.

The intellectual merit of the work is embodied in its addressing a fundamentally challenging topic: how to capture complicated multiscale phenomena with computational tools in a fashion which respects both the underlying mathematics as well as experimental observation. For non-linear multiscale problems, these answers are not easy; however, their understanding is critical in areas of importance to the nation where rigorous predictive tools are now being used. Specific examples include flood and storm surge dynamics, groundwater contaminant flow, human blood circulation response to surgical interventions, combustion and fire safety, response of civilian infrastructure such as bridges and roads to stimuli, as well as a variety of aerospace applications. The workshop will bring together some of the world's leading experts in a diverse set of fields in the physical, mathematical, and computational sciences. The broader impacts of the Workshop are clear as well. Since decision-makers and leaders, and thus society at large, are relying more and more on computational methods to aid in decision-making process, it is in the interest of all that the predictions of these methods can be used with confidence by non-experts. The Workshop will raise awareness in a variety of key scientific communities of some of the critical issues and methods for verification and validation. Additionally, the Workshop will seek participation from a broad range of the scientific community by making available NSF-supported travel grants to members of under-represented groups.

Project Report

was held on the campus of the University of Notre Dame on 17-19 October 2011. The Workshop brought together seventy scientists and engineers from across the nation to discuss strategies for accurate prediction of natural phenomena. It is widely recognized that computers are being used to predict the behavior of many disparate systems, including the weather, performance of aircraft, structural response to earthquakes, bio-medical phenomena, and financial markets. These predictions are typically based on underlying mathematical models of the system behavior. And the predictions are never perfect. The topic of the Workshop was to scientifically address the reasons for why our predictions are not perfect and to discuss ways to systematically improve those predictions. The reasons for imperfection are many and can include: 1) the computational model fails to accurately mimic the underlying mathematical model, 2) the underlying mathematical model itself fails to accurately mimic nature. Correcting 1) is the topic of "Verification", and correcting 2) is the topic of "Validation." Both exercises are necessary in order for decision-makers to have confidence in the predictions of computational scientists in order to guide their decisions on matters ranging from whether to evacuate cities in the face of a hurricane storm surge or whether a underground hazardous storage facility will be safe for future generations. These topics were discussed in detail at the Workshop. The most important outcome was that a group of researchers from disparte fields, but with a common interest in V&V, were able to interact in a common forum so as hone their skills and glean new insights which they could bring to their individual disciplines.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Junping Wang
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University of Notre Dame
Notre Dame
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