Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian and Tensor Properties

Advances in artificial intelligence (AI) are significantly transforming and accelerating discoveries in materials science and enabling our understanding of materials systems across various spatial and temporal scales. Here we focus on the predictions of quantum Hamiltonian and tensor properties of materials, which are particularly important for quantum chemistry, condensed matter physics, and materials science. First we will present QHNet – an SE(3)-equivariant and efficient graph network, which not only obeys the underlying symmetries, but also significantly reduce the tensor products and avoids the exponential growth of channel dimensions with increasing atom types. The results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed and less memory requirement due to its streamlined architecture. Second, we will present GMTNet – a space group symmetry informed network for O(3)-equivariant crystal tensor prediction. GMTNet is specifically designed for predicting tensor properties of materials such as dielectric, piezoelectric, and elastic tensors. The results show that our GMTNet not only achieves promising performance on crystal tensors of various orders, but also generates predictions fully consistent with the intrinsic crystal symmetries. Finally, we will briefly introudce QH9 – A quantum Hamiltonian prediction benchmark for QM9 molecules, with 130,831 stable molecular geometries, highly valuable for developing machine learning methods and accelerating materials design for scientific and technological applications.