Adaptive construction of surrogate functions for various computational mechanics models

In most science and engineering fields, numerical simulation models are often used to replicate physical systems. An attempt to imitate the true behavior of complex systems results in computationally expensive simulation models. The models are more often than not associated with a number of parameters that may be uncertain or variable. Propagation of variability from the input parameters in a simulation model to the output quantities is important for better understanding the system behavior. Variability propagation of complex systems requires repeated runs of costly simulation models with different inputs, which can be prohibitively expensive. Thus for efficient propagation, the total number of model evaluations needs to be as few as possible. An efficient way to account for the variations in the output of interest with respect to these parameters in such situations is to develop black-box surrogates. It involves replacing the expensive high-fidelity simulation model by a much cheaper model (surrogate) using a limited number of the high-fidelity simulations on a set of points called the design of experiments (DoE). The obvious challenge in surrogate modeling is to efficiently deal with simulation models that are expensive and contains a large number of uncertain parameters. Also, replication of different types of physical systems results in simulation models that vary based on the type of output (discrete or continuous models), extent of model output information (knowledge of output or output gradients or both), and whether the model is stochastic or deterministic in nature. All these variations in information from one model to the other demand development of different surrogate modeling algorithms for maximum efficiency. In this dissertation, simulation models related to application problems in the field of solid mechanics are considered that belong to each one of the above-mentioned classes of models. Different surrogate modeling strategies are proposed to deal with these models and their performance is demonstrated and compared with existing surrogate modeling algorithms. The developed algorithms, because of their non-intrusive nature, can be easily extended to simulation models of similar classes, pertaining to any other field of application