I came to this paper looking for a way to move beyond using a MLIP model's latent space as a feature vector to represent a material in a computational inexpensive way.
The accurate modeling of spin-orbit coupling (SOC) effects in diverse complex systems remains a significant challenge due to the high computational demands of density functional theory (DFT) and the limited transferability of existing machine-learning frameworks. This study addresses these limitations by introducing Uni-HamGNN, a universal SOC Hamiltonian graph neural network that is applicable across the periodic table. By decomposing the SOC Hamiltonian into spin-independent and SOC correction terms, our approach preserves SU(2) symmetry while significantly reducing parameter requirements. Based on this decomposition, we propose a delta-learning strategy to separately fit the two components, thereby addressing the training difficulties caused by magnitude discrepancies between them and enabling efficient training. The model achieves remarkable accuracy (mean absolute error of 0.0025 meV for the SOC-related component) and demonstrates broad applicability through high-throughput screening of the GNoME dataset for topological insulators, as well as precise predictions for 2D valleytronic materials and transition metal dichalcogenide (TMD) heterostructures. This breakthrough eliminates the need for system-specific retraining and costly SOC-DFT calculations, paving the way for rapid discovery of quantum materials.
It was clear when trying to build a model to predict magnetocrystalline anisotropy energy (MAE) that MLIPs don't have what we're looking for.
The physics that drives the property are well understood. Spin-orbit coupling is at the heart of the phenomenon. Let's dive into this paper and see if it would be a suitable model to learn a material representation we can use to predict/derive this kind of magnetic property.
This paper and this model are a v2 expansion of a prior universal GNN Hamiltonian prediction model (HamGNN). You can check out that paper here:
While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the Kohn–Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations. Despite advancements, challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist. Addressing these hurdles, this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project. We demonstrate its generality in predicting electronic structures across the whole periodic table, including complex multi-elemental systems, solid-state electrolytes, Moiré twisted bilayer heterostructure, and metal-organic frameworks. Moreover, we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets, identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands. By offering a reliable efficient framework for computing electronic properties, this universal Hamiltonian model lays the groundwork for advancements in diverse fields, such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible. This paper corresponds to HamGNN v1 and the universal model weights released in 2024. https://iopscience.iop.org/article/10.1088/0256-307X/41/7/077103
This v1 paper doesn't cover much. It's a great development and grounding for v2, but it's mostly about introducing the model and a quick look at some predictions on different materials.
They published the weights to this v1 model and I was able to get it working. Pretty cool! I'm new to having this level of theory and working with the richness of a material's Hamiltonian. More will be coming along this line of work soon. I didn't fully understand it before going into it, but the way I wanted to use the model (spin-orbit coupling and first principles calculation of MAE) was not supported. This new v2 model does support it though. Makes sense that they explicitly call out that it's a "spin-orbit-coupled" Hamiltonian model.
Here are some resources to check out beyond these papers:
Some random, interesting snippets on the difficulties of this problem:
generating SOC Hamiltonian training sets involves computationally intensive DFT calculations that include SOC, which are approximately eight times slower than their non-SOC counterparts
incorporating SOC transforms Hamiltonians into complex-valued matrices with quadrupled dimensions, dramatically expanding the parameter space.
the two-orders-of-magnitude disparity between SOC and non-SOC matrix elements can lead to training instability, as conventional neural networks struggle to discern the subtle contributions of SOC in the presence of dominant spin-independent terms
To overcome these challenges, the authors employ a delta-learning strategy that splits the non-SOC Hamiltonian from the SOC Hamiltonian.
Our work addresses these challenges through a physics-informed decomposition strategy that separates SOC Hamiltonians into spin-independent components and symmetry-preserving correction terms. This method not only reduces the number of required parameters but also rigorously maintains SU(2) symmetry, thereby enabling a delta-learning framework capable of independently optimizing magnitude-disparate terms in separate channels.
They mention the scale of the dataset they used to train the model, and compared to v1 it's quite a bit smaller.
The resulting universal SOC Hamiltonian model, termed Uni-HamGNN, was trained using a resource-efficient dataset containing only 10,000 SOC matrices supplemented by 40,000 computationally economical non-SOC matrices.
Compare this to almost the full set of Materials Project material's DFT codes, which is closer to 500,000. I wonder if they initialized the model with the weights of v1 for channel 1, the spin-independent block.
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