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  • Machine learning has made significant progress in being used as an augmented tool to progress research in many scientific fields. One such area is the field of quantum chemistry where machine learning methods have been employed to accelerate calculations by replacing high cost quantum chemistry computations with trained machine learning models. While this has significantly reduced the computational resource usage in making new calculations, there still remains the high cost of generating high accuracy, or high fidelity, training data for such models. This new overhead can be mitigated by the use of multifidelity methods which reduces the cost of training data required to achieve a certain model accuracy.This compiled-format dissertation develops and studies the use of multifidelity methods with machine learning for the prediction of quantum chemical properties. The Multifidelity Machine Learning approach is developed as a time-efficient alternative to the single fidelity machine learning methods. Novel methodological developments such as optimized Multifidelity Machine Learning and the $\Gamma$-curve are developed in this dissertation to demonstrate that low-cost high-accuracy machine learning for quantum chemistry is a viable option with multifidelity approaches. The benefit of using such multifidelity models for the prediction of several quantum chemistry properties ranging from atomization energies to excitation energies is benchmarked. Assessments in terms of cost of generating training data versus model accuracy of several multifidelity models are studied for the prediction of diverse quantum chemistry properties. In addition, a multifidelity benchmark dataset with computational time-costs is generated for the benchmarking of multifidelity models and for future development in this field. The effect of the multifidelity data hierarchy on model accuracy and the time-cost efficiency of several multifidelity models is also studied to provide a comprehensive outlook on the use of multifidelity methods for quantum chemical properties. Two specific applications using the herein developed multifidelity methods are presented. The first, prediction of ground state energies of several small monomers which are atmospherically relevant, is used as an additional assessment of the efficiency of the multifidelity methods in comparison to existing state of art machine learning methods used in quantum chemistry. Second, the novel $\Gamma$-curve is applied to predicting excitation energies of a 16 porphyrin molecules over a 40 pico-second trajectory at a high fidelity quantum chemical method showing significant reduction in the cost incurred to train the machine learning model without sacrificing accuracy. Finally, conclusions are drawn about the efficiency of multifidelity machine learning methods for use in quantum chemistry. Extensions of the use of optimized MFML and the $\Gamma$-curve method are discussed in order to direct future research arising from the works of this dissertation.
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