Advanced material systems refer to materials that are comprised of multiple traditional constituents but complex microstructure morphologies, which lead to their superior properties over conventional materials. This dissertation is motivated by the grand challenge in accelerating the design of advanced material systems through systematic optimization with respect to material microstructures or processing settings. While optimization techniques have mature applications to a large range of engineering systems, their application to material design meets unique challenges due to the high dimensionality of microstructures and the high costs in computing process-structure-property (PSP) mappings. The key to addressing these challenges is the learning of material representations and predictive PSP mappings while managing a small data acquisition budget. This dissertation thus focuses on developing learning mechanisms that leverage context-specific meta-data and physics-based theories. Two research tasks will be conducted: In the first, we develop a statistical generative model that learns to characterize high-dimensional microstructure samples using low-dimensional features. We improve the data efficiency of a variational autoencoder by introducing a morphology loss to the training. We demonstrate that the resultant microstructure generator is morphology-aware when trained on a small set of material samples, and can effectively constrain the microstructure space during material design. In the second task, we investigate an active learning mechanism where new samples are acquired based on their violation to a theory-driven constraint on the physics-based model. We demonstrate using a topology optimization case that while data acquisition through the physics-based model is often expensive (e.g., obtaining microstructures through simulation or optimization processes), the evaluation of the constraint can be far more affordable (e.g., checking whether a solution is optimal or equilibrium). We show that this theory-driven learning algorithm can lead to much improved learning efficiency and generalization performance when such constraints can be derived. The outcomes of this research is a better understanding of how physics knowledge about material systems can be integrated into machine learning frameworks, in order to achieve more cost-effective and reliable learning of material representations and predictive models, which are essential to accelerate computational material design.

ABSTRACT A vortex tube is a device of a simple structure with no moving parts that can be used to separate a compressed gas into a hot stream and a cold stream. Many studies have been carried out to find the mechanisms of the energy separation in the vortex tube. Recent rapid development in computational fluid dynamics is providing a powerful tool to investigate the complex flow in the vortex tube. However various issues in these numerical simulations remain, such as choosing the most suitable turbulent model, as well as the lack of systematic comparative analysis. LES model for the vortex tube simulation is hardly used in the present literatures, and the influence of parameters on the performance of the vortex tube has scarcely been studied. This study is aimed to find the influence of various parameters on the performance of the vortex tube, the best geometric value of vortex tube and the realizable method to reach the required cold out flow rate 40 kg/s . First of all, setting up an original 3-D simulation vortex tube model. By comparing experiment results reported in the literature and our simulation results, a most suitable model for the simulation of the vortex tube is obtained. Secondly, we perform simulations to optimize parameters that can deliver a set of desired output, such as cold stream pressure, temperature and flow-rate. We also discuss the use of the cold air flow for petroleum engineering applications.