Non-intrusive multi-fidelity parametric reduced order model for industrial problems

Industrial problems often involve parametric design and deal with complex computational models or expensive experimental measurements. The study of multiple design configurations, such as optimization or uncertainty quantification, can become prohibitive, especially when the number of observations becomes too high. Consequently, there is a profound interest in lowering the computational cost of parametric problems. Surrogate models, as interpolations or regression models, are a great solution to this issue, as they allow for learning a map between the input parameter space and the corresponding outputs. They usually approximate problem-specific quantities of interest, and their training is relatively inexpensive. Nevertheless, if the quantity of interest is not a scalar value, but it is a vector quantity, most regression models have a limited range of application, especially if the vector space is high-dimensional. This is the case for numerical simulation solutions, such as those for Computational Fluid Dynamics (CFD) or structural Finite Element Models (FEM), where the quantities of interest are vector fields, e.g., velocity or pressure fields. It would not be feasible to approximate an industrially relevant parametric solution with a single regression model due to the model’s limitations. Reduced Order Models (ROM) aim to solve exactly this problem. They operate a dimensionality reduction of the vector fields, here called snapshots, by encoding them with Proper Orthogonal Decomposition (POD). Successively, the obtained snapshots’ latent representation is exploited to predict unseen design configurations. In this work, a novel non-intrusive multi-fidelity ROM has been developed to address the high offline computational cost of classical ROMs. Low-fidelity (LF) information is exploited to improve the high-fidelity (HF) knowledge of the problem in a multi-fidelity manner. In particular, the proposed multi-fidelity ROM has been designed to handle industrial applications, while favoring the automation of the process. The first part of the thesis discusses the methodological core of the work. Starting from ROMs, to regression models, their relationship is deepened, specifically for the non-intrusive ROM formulations. Successively, multi-fidelity regression models are introduced, illustrating how different approaches to multi-fidelity techniques work. Finally, the novel non-intrusive multi-fidelity ROM is presented, combining the previous methods. The multi-fidelity ROM has two main characteristics: a mixed fidelity snapshot matrix and the use of a multi-fidelity regression model, i.e., the Nonlinear AutoRegressive multi-fidelity Gaussian Process (NARGP). The mixed fidelity snapshots enrich the POD basis functions, increasing the capability to represent unseen snapshots, while the NARGP improves the accuracy of the POD latent predictions through the addition of LF snapshots. The second part of the thesis shows how the multi-fidelity ROM performs in industrially relevant use cases and what the main challenges are. External aerodynamics and internal flows are both considered, and different types of parameterizations are examined, ranging from geometrical to operational input variables. Many query applications are considered, e.g., uncertainty quantification, highlighting the potential of ROMs in these fields. Moreover, the problem of non-coherent snapshots due to different fidelity snapshots and large geometrical deformations is addressed in the proposed applications. In general, all the results are compared to equivalent single-fidelity ROMs to perform a meaningful comparison.