Verification, Validation, and Uncertainty Quantification for Predictive Modeling in Computational Mechanics

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Computational predictions are increasingly used in science and engineering as a basis for critical decision making. It is thus becoming important to quantify, and possibly reduce, uncertainties in output quantities of computer simulations, as uncertainties usually arise from the use of imperfect physical models and from limited availability of data. The proposed research program aims at developing new theories, methodologies, and algorithms for predictive modeling, a term that has recently emerged in the literature to describe the systematic use of all relevant information to enhance the predictive power of theoretical and computational models. Applications will be in computational mechanics with a special focus on multi-scale and multi-physics modeling. Predictive modeling encompasses topics such as model validation, verification, and uncertainty quantification (UQ). Code and Solution Verification is the process of determining whether a computational model produces predictions with sufficient accuracy for meaningful comparisons with experimental data. Validation is the process of determining the accuracy by which a mathematical model can predict physical events with respect to a decision that has to be made. Finally, UQ is the process by which one characterizes all uncertainties in a system and its outputs. Validation and UQ are intimately related since the treatment of uncertainty involves three distinct processes: 1) the statistical estimation of random model parameters; 2) the validation process, which aims at determining, if only subjectively, whether or not the hypotheses of the model would hold for predictions of interest; 3) the propagation of input uncertainties through the stochastic system to quantify the uncertainties in quantities of interest. Outcomes of the proposed research program will be a collection of computational tools for a posteriori error estimation of discretization and modeling errors, adaptive schemes for multi-scale and multi-physics simulations, guidelines for model validation, including among others, planning, analysis of acceptance metrics, experimental design to select optimal data sets for calibration and validation, data quality assessment.