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Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph…

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant…

Modern microelectronic devices are composed of interfaces between a large number of materials, many of which are in amorphous or polycrystalline phases. Modeling such non-crystalline materials using first-principles methods such as density…

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still…

This paper studies the problem of learning the large-scale Gaussian graphical models that are multivariate totally positive of order two ($\text{MTP}_2$). By introducing the concept of bridge, which commonly exists in large-scale sparse…

Graph Transformers have recently attracted attention for molecular property prediction by combining the inductive biases of graph neural networks (GNNs) with the global receptive field of Transformers. However, many existing hybrid…

Graph neural networks (GNNs) have achieved success in various inference tasks on graph-structured data. However, common challenges faced by many GNNs in the literature include the problem of graph node embedding under various geometries and…

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML…

Retrosynthesis prediction is one of the fundamental challenges in organic chemistry and related fields. The goal is to find reactants molecules that can synthesize product molecules. To solve this task, we propose a new graph-to-graph…

When speaking about molecular electronics, the obvious question which occurs is how does one study it theoretically. The simplest theoretical model suitable for application in molecular electronics is the two dimensional Hubbard model. The…

Hybrid density functional calculation is indispensable to accurate description of electronic structure, whereas the formidable computational cost restricts its broad application. Here we develop a deep equivariant neural network method…

We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…

We propose Hamiltonian Quantum Generative Adversarial Networks (HQuGANs), to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the…

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…

Deep learning systems have been successfully applied to Euclidean data such as images, video, and audio. In many applications, however, information and their relationships are better expressed with graphs. Graph Convolutional Networks…

A deep understanding of the intricate interactions between particles within a system is a key approach to revealing the essential characteristics of the system, whether it is an in-depth analysis of molecular properties in the field of…

Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms, where they emerge as effective descriptions of strongly correlated phases and engineered dynamics. We introduce a…

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…

Graph convolutional networks (GCNs) have received considerable research attention recently. Most GCNs learn the node representations in Euclidean geometry, but that could have a high distortion in the case of embedding graphs with…

We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…