报告时间：9月29日周五上午10:00—11:00
报告地点：统计楼105
Some Statistical Aspects of Uncertainty Quantification
Peter Chien, University of Wisconsin-Madison
Computer simulations based on computational fluid dynamics, finite element analysis, discrete element models and multi-physics codes are widely used in aerospace, turbomachine, finance, data centers and many other fields. These simulations are necessary for studying complex phenomena such as thermal dynamics, supersonic flows, aircraft-controller interaction, and engine systems. Unfortunately, simulation models are never perfect and various uncertainties, including random initial and boundary conditions, input uncertainty, and model discrepancy, can produce misleading results. Thus, it is necessary to develop a rigorous mathematical framework for uncertainty quantification (UQ). UQ is an emerging field in applied mathematics, statistics and engineering. The benefits of modeling and simulation have been recognized at a policy level, and requirements for the application of UQ in modeling and simulation are beginning to be adopted by regulatory agencies such as the US Food and Drug Administration (FDA).
This talk consists of two statistical aspects of UQ. The first topic discusses UQ for simulations with invariance properties, which appear in materials science, physics and biology. We propose a new statistical framework for building emulators to preserve invariance. The framework uses a weighted complete graph to represent the geometry and introduces a new class of function, called the relabeling symmetric functions, associated with the graph. The effectiveness of the method is illustrated by several examples from materials science. The second topic deals with computer codes with gradients. The gradient-enhanced Gaussian process emulator is widely used to analyze all outputs from a computer model with gradient info. The gradient-enhanced Gaussian process emulator has more numeric problems than in many multivariate cases because of the dependence of the model output and each gradient output.We derive a statistical theory to understand why this problem happens.