Towards a Universal Model for the Electronic Density of States

The electronic density of states (DOS) is a fundamental property in materials science that quantifies the distribution of available electronic states. The DOS is a particularly useful descriptor for materials discovery as it underlies many properties of a material, such as its conductivity, band gap or electronic heat capacity. However, the computation of the DOS through quantum mechanical calculations is costly, hindering its applicability for large systems typically encountered in materials discovery. Machine learning has been shown to be a promising alternative to accelerate quantum mechanical calculations. Although significant efforts have been dedicated to predict the energies and forces of a material, there has not been comparable advancements in predicting the DOS.

This thesis bridges this research gap by developing a new machine learning framework that is aligned to the underlying physics of the DOS. The framework addresses the ill-defined energy reference in DOS calculations by optimizing the energy reference during training. This adaptive reference framework aligns the common spectral patterns in the dataset, allowing the model to better predict the finer features of the DOS while remaining unaffected by arbitrary numerical offsets. This adaptive reference framework is shown to produce models that can compute the DOS and its secondary properties with higher accuracy and can better generalize to larger systems. The framework is then extended to train a Point Edge Transformer (PET) using the highly chemically diverse Massive Atomistic Diversity (MAD) dataset. To account for the significant energy truncation within the MAD dataset, the framework is modified to handle the large variations in energy truncation across the dataset. The resulting model, PET-MAD-DOS, is able to generalize well across vast chemical spaces, providing qualitative performance compared to specialized models. Furthermore, PET-MAD-DOS shows immense promise as a foundation model for fine-tuning, achieving competitive performance relative to specialized models using a fraction of the data whilst maintaining its generalizability.

A remaining challenge in DOS modeling is the high sensitivity of secondary quantities to model noise in the DOS. This thesis proposes two approaches to alleviate this. One approach relies on a handcrafted denoising algorithm while another relies on a data-driven approach to directly predict the secondary quantities from the DOS spectra. While the data-driven approach is more accurate, the denoising approach offers a compromise between accuracy and physical interpretability of the DOS. Further suggestions have been proposed at the end for potential directions to address this challenge.

Overall, the thesis provides a performant framework for learning the DOS using machine learning and adapts it to develop a universal model for the DOS. The framework demonstrates the significance and benefits of building a machine learning workflow that is ada