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Bayesian approach to alloy simulation, A
Novick, Andrew
Novick, Andrew
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2024
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Abstract
Alloy simulation is—seemingly—rife with intractable mathematical problems: the combinatorial explosion of atomic decorations, the irreducible global nature of convex hulls, and the curse of dimensionality in configuration space. Due to the importance of alloys across materials science, considerable attention has been given to surmounting these computational obstacles. The typical angle is to tackle daunting mathematical problems with increasingly complex model-Hamiltonians, ranging from lattice models to machine-learned interatomic potentials. Even in the fortunate cases where these models provide accurate predictions, extracting insight from large-scale simulation is challenging, limiting our theoretical understanding.
Herein, I take a Bayesian approach to alloy simulation. All predictions provided from calculations are thus represented as probabilistic distributions over possible outcomes rather than isolated, singular values. The classic materials science questions are used to ground this thesis: i) can a given chemical composition be made as a single-phase alloy; and ii) what will be its local and long-range atomic structure? Equipped with Bayesian modeling, I show that relatively few calculations are necessary to provide sufficient estimations for the stated questions. As such, advanced alloy simulation is returned to the domain of first-principles calculations, enabling accuracy and functionality. While I focus solely on first-principles simulation, model-Hamiltonian research also stands to benefit from the developed Bayesian approach, which could accelerate exploration across time scales, length scales, and composition spaces. If there is an overarching thesis to this amalgamation of work, it is the following. Bloated mathematical constructs conceal the underlying simplicity of alloys—through the success of relatively simple simulation, I highlight the elegance within these disordered materials.
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