ML-DFT: Powering Machine-Learning With Density Functional Theory - Monaghan, Eoin (Trinity College Dublin. School of Physics. Discipline of Physics, 2026)
This thesis investigates machine-learning force field development for atomic systems, progressing from molecular structures through periodic materials towards high-entropy alloy modelling. We develop equivariant graph neural network architectures leveraging density functional theory to predict atomic forces with near-quantum mechanical accuracy whilst achieving substantial computational efficiency. We establish a rigorous set of data generation methodologies based on the MD17 dataset, and train models which yield force predictions with R2-scores exceeding 0.98 for a variety of molecules. The central contribution establishes fundamental node alignment failures arising from interfacing equivariant distance-metric representations with neural networks. Through group-theoretic analysis, we demonstrate that molecular symmetries generate representational degeneracies due to the introduction of neural networks. We develop quantitative ambiguity metrics combining automorphism group cardinalities with structural complexity, revealing strong correlations with model performance. This transforms symmetry considerations into actionable pre-screening tools, whilst revealing that high-symmetry molecules counterintuitively impose systematic training difficulties. Extension to periodic systems reveals fundamental limitations for heterogeneous datasets. We integrate echo state network principles into Ni-Pd alloy systems, yielding exceptional energy predictions, whilst custom interpolation schemes produce force calculations rivalling backpropagation methods. This work establishes theoretical frameworks identifying symmetry-induced training difficulties whilst offering pathways toward improved efficiency and accuracy for high-entropy alloy research.
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Keywords: Graph Neural Networks; Machine-Learning; Message Passing; Density Functional Theory; Machine-Learning Interatomic Potentials