Multi-fidelity Data Fusion with Uncertainty Quantification

In many applications in engineering and sciences analysts have simultaneous access to multiple data sources. In such cases, the overall cost of acquiring information can be reduced via data fusion or multi-fidelity (MF) modeling where one leverages inexpensive low-fidelity (LF) sources to reduce the reliance on expensive high-fidelity (HF) data. In this thesis we present two main contributions in the field of data fusion and its application in engineering. In particular, we introduce: (1) a novel neural network (NN) architecture for data fusion under uncertainty, namely Probabilistic Neural Data Fusion (Pro-NDF), and (2) a MF calibration scheme based on Latent Map Gaussian Processes (LMGPs) for fracture modelling of metallic components via reduced-order models (ROMs). In the context of building an emulator for data fusion under uncertainty, we introduce Pro-NDF, a novel NN architecture that converts MF modeling into a nonlinear manifold learning problem. Pro-NDF inversely learns non-trivial (e.g., non-additive and nonhierarchical) biases of the LF sources in an interpretable and visualizable manifold where each data source is encoded via a low-dimensional distribution. This probabilistic manifold quantifies model form uncertainties such that LF sources with small bias are encoded close to the HF source. Through a set of analytic and engineering examples, we demonstrate that our approach provides a high predictive power while quantifying various sources of uncertainty.In the context of fracture modelling of metallic materials with microscopic pores, we propose a data-driven framework that integrates a mechanistic ROM with a MF calibration scheme based on LMGPs. The proposed ROM offers computational speedup compared to direct numerical simulations (DNS) by solving a reduced-order representation of the governing equations and reducing the degrees of freedom via clustering. Since clustering affects local strain fields and hence the fracture response, we employ LMGPs to calibrate the damage parameters of an ROM as a function of microstructure and clustering, i.e., fidelity level, such that the ROM (i.e., LF source) faithfully emulates DNS (i.e., HF source). We demonstrate the application of our MF framework in predicting the damage behavior of a multiscale metallic component with spatially varying porosity. Our results indicate that microstructural porosity can significantly affect the performance of macro-components and hence must be considered in the design process.