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For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through…

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous.…

Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN…

Graph neural networks (GNNs) have achieved remarkable success in a variety of machine learning tasks over graph data. Existing GNNs usually rely on message passing, i.e., computing node representations by gathering information from the…

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave…

This work proposes a new approach for mapping GPU threads onto a family of discrete embedded 2D fractals. A block-space map $\lambda: \mathbb{Z}_{\mathbb{E}}^{2} \mapsto \mathbb{Z}_{\mathbb{F}}^{2}$ is proposed, from Euclidean parallel…

Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features…

We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

Discovering human cognitive and emotional states using multi-modal physiological signals draws attention across various research applications. Physiological responses of the human body are influenced by human cognition and commonly used to…

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory…

Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking…

Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…

We developed a graph-based block-diagonalization (GBBD) method for the full configuration interaction Hamiltonian of molecular systems to efficiently calculate the exact eigenvalues of low-energy states. In this approach, the non-zero…

Towards developing effective and efficient brain-computer interface (BCI) systems, precise decoding of brain activity measured by electroencephalogram (EEG), is highly demanded. Traditional works classify EEG signals without considering the…

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…