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Design space exploration (DSE) is used to improve and understand engineering designs. Such designs must meet objectives and structural requirements. Design improvement is non-trivial and requires new DSE methods. Turbomachinery manufacturers must continue to improve existing engines to keep up with global demand. Two challenges of turbomachinery DSE are: the time required to evaluate designs, and knowing which designs to evaluate. This research addressed these challenges by developing novel surrogate and principal component analysis (PCA) based DSE methods. Node and PCA-based surrogates were created to allow faster DSE of turbomachinery blades. The surrogates provided static stress estimation within 10% error. Surrogate error was related to the number of sampled finite element (FE) models used to train the surrogate and the variables used to change the designs. Surrogates were able to provide structural evaluations three to five orders of magnitude faster than FEA evaluations. The PCA-based surrogates were then used to create a PCA-based design workflow to help designers know which designs to evaluate. The workflow used either two-point correlation or stress and geometry coupling to relate the design variables to principal component (PC) scores. These scores were projections of the FE models onto the PCs obtained from PCA. Analysis showed that this workflow could be used in DSE to better explore and improve designs. The surrogate methods were then applied to vibratory stress. A computationally simplified analysis workflow was developed to allow for enough fluid and structural analyses to create a surrogate model. The simplified analysis workflow introduced 10% error but decreased the computational cost by 90%. The surrogate methods could not directly be applied to emulation of vibration due to the large spikes which occur near resonance. A novel, indirect emulation method was developed to better estimate vibratory responses Surrogates were used to estimate the inputs to calculate the vibratory responses. During DSE these estimations were used to calculate the vibratory responses. This method reduced the error between the surrogate and FEA from 85% to 17%. Lastly, a PCA-based multi-fidelity surrogate method was developed. This assumed the PCs of the high and low-fidelities were similar. The high-fidelity FE models had tens of thousands of nodes and the low-fidelity FE models had a few hundred nodes. The computational cost to create the surrogate was decreased by 75% for the same errors. For the same computational cost, the error was reduced by 50%. Together, the methods developed in this research were shown to decrease the cost of evaluating the structural responses of turbomachinery blade designs. They also provided a method to help the designer understand which designs to explore. This research paves the way for better, and more thoroughly understood turbomachinery blade designs.

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<p>A wide range of optoelectronic applications demand semiconductors optimized for purpose.</p> <p>My research focused on data-driven identification of ABX3 Halide perovskite compositions for optimum photovoltaic absorption in solar cells.</p> <p>I trained machine learning models on previously reported datasets of halide perovskite band gaps based on first principles computations performed at different fidelities.</p> <p>Using these, I identified mixtures of candidate constituents at the A, B or X sites of the perovskite supercell which leveraged how mixed perovskite band gaps deviate from the linear interpolations predicted by Vegard's law of mixing to obtain a selection of stable perovskites with band gaps in the ideal range of 1 to 2 eV for visible light spectrum absorption.</p> <p>These models predict the perovskite band gap using the composition and inherent elemental properties as descriptors.</p> <p>This enables accurate, high fidelity prediction and screening of the much larger chemical space from which the data samples were drawn.</p> <p><br></p> <p>I utilized a recently published density functional theory (DFT) dataset of more than 1300 perovskite band gaps from four different levels of theory, added to an experimental perovskite band gap dataset of \textasciitilde{}100 points, to train random forest regression (RFR), Gaussian process regression (GPR), and Sure Independence Screening and Sparsifying Operator (SISSO) regression models, with data fidelity added as one-hot encoded features.</p> <p>I found that RFR yields the best model with a band gap root mean square error of 0.12 eV on the total dataset and 0.15 eV on the experimental points.</p> <p>SISSO provided compound features and functions for direct prediction of band gap, but errors were larger than from RFR and GPR.</p> <p>Additional insights gained from Pearson correlation and Shapley additive explanation (SHAP) analysis of learned descriptors suggest the RFR models performed best because of (a) their focus on identifying and capturing relevant feature interactions and (b) their flexibility to represent nonlinear relationships between such interactions and the band gap.</p> <p>The best model was deployed for predicting experimental band gap of 37785 hypothetical compounds.</p> <p>Based on this, we identified 1251 stable compounds with band gap predicted to be between 1 and 2 eV at experimental accuracy, successfully narrowing the candidates to about 3% of the screened compositions.</p>