Computational Methods for Verification and Validation with Applications in Mechanics

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Computational Sciences and Engineering, the discipline which focuses on computer simulations of physical phenomena and engineering systems, has gained great maturity over the years to the point that it is today widely considered for design and decision-making, either for material sciences, aerospace applications, weather-related disaster monitoring, control of manufacturing processes, etc. Yet, it is also acknowledged that confidence in computer predictions is often limited because of the imperfect knowledge of the mathematical models and their parameters. In fact, due to the complexity of the multiphysics and multiscale systems being simulated, it is, more than ever, essential to ensure that predictions be quantitatively reliable. The computational models need to be extensively subjected to verification and validation processes in order to assess the credibility of the simulation results. Code and Solution Verification is the process of determining whether computational models produce numerical results with sufficient accuracy for meaningful comparisons with experimental data. Validation is the process of determining the accuracy by which mathematical models can predict physical events with respect to a decision that has to be made. The topics of verification and validation are not new, but approaches and methodologies currently available still pertain more to an art, especially in the case of validation, than to a scientific approach. The proposed research program aims at developing new theories, methodologies, and algorithms for predictive modeling, and will concentrate on the following objectives: 1) Construction of adaptive and verified reduced-order models (low rank approximations, proper orthogonal decomposition, etc.) with respect to specific quantities of interest, the goal being to obtain surrogate models for fast and accurate statistical characterization of output quantities of interest; 2) Use of machine learning methods to enhance the information content of datasets for parameter inference and model validation in the case of scarce data (e.g. neural networks, deep learning, model selection, cross-validation, resampling methods, etc.); 3) Application of graphical methods to assess the relevance in the choice of validation scenarios and data to properly exercise a model. The methodologies developed in the project will be tested on several applications of engineering interest. Outcomes of the project will be a collection of computational tools for verification and validation of computational models. The originality of the work will be the development of reduced-order models tailored to the calculation of quantities of interest and the integration of machine learning techniques to enhance the reliability of validation processes. The project should have an impact not only in the field of computational mechanics but also in any other engineering applications that heavily rely on computer simulations of complex physical phenomena.