We propose a framework to combine strong non-linear expressiveness with strict SO(3)-equivariance in prediction of the electronic-structure Hamiltonian, by exploring the mathematical relationships between SO(3)-invariant and SO(3)-equivariant quantities and their representations. The proposed framework, called TraceGrad, first constructs theoretical SO(3)-invariant trace quantities derived from the Hamiltonian targets, and use these invariant quantities as supervisory labels to guide the learning of high-quality SO(3)-invariant features. Given that SO(3)-invariance is preserved under non-linear operations, the learning of invariant features can extensively utilize non-linear mappings, thereby fully capturing the non-linear patterns inherent in physical systems. Building on this, we propose a gradient-based mechanism to induce SO(3)-equivariant encodings of various degrees from the learned SO(3)-invariant features. This mechanism can incorporate powerful non-linear expressive capabilities into SO(3)-equivariant features with correspondence of physical dimensions to the regression targets, while theoretically preserving equivariant properties, establishing a strong foundation for predicting electronic-structure Hamiltonian. Experimental results on eight challenging benchmark databases demonstrate that our method achieves state-of-the-art performance in Hamiltonian prediction.

Both point cloud-based and view-based deep learning methods for 3D shape recognition have achieved relatively remarkable results in recent years. However, there are few methods to jointly represent 3D shapes from both point cloud and multi-view modal data. Therefore, we propose a guidance enhancement network (GENet) for 3D shape recognition based on multimodal data. On the one hand, the point cloud is encoded with features from both explicit and implicit aspects, and on the other hand, all views are encoded and constructed as a graph. In the multilayer guidance enhancement module, graph convolutional neural network (GCN) enhances each view feature, and then temporary high-level features (initially point cloud global feature) guide multiple low-level view features to obtain correlation coefficients, through which the views with higher importance are filtered as inputs for the next layer of the structure and the view features in the current layer are weighted and aggregated. The aggregated view features are then connected to the high-level features with residuals to form the enhanced high-level features. The 3D shape descriptor is finally obtained after several guidance and enhancements. The proposed GENet achieves state-of-the-art results on the 3D benchmark dataset ModelNet.

Both point cloud-based and multi-view-based methods have achieved remarkable results in 3D shape recognition, yet there are few methods that combine the two types of data. In this paper, a novel Global-Local Complementary Network (GLCNet) based on multimodal data is proposed. The network obtains more powerful shape descriptors by stacking multiple layers of Global-Local Complementary Module (GLC Module). More specifically, the Global-Local Relation Score Module is first used to obtain the relationship between view features and global feature. The relationship is then utilized to facilitate the aggregation of view features and to filter out the more important ones. Finally, the aggregated view features are fused with the global features to form a stronger global feature. GLCNet enables the characteristics of various data to be fully utilized and achieves a true sense of complementarity of strengths and weaknesses. Extensive experiments on the benchmark dataset ModelNet show that GLCNet achieves state-of-the-art results in 3D shape classification and retrieval.

Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.

Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-$1/2$$J_1-J_2$Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNN’s translational invariance, we successfully investigate the quantum system with the lattice size up to$24\times 24$, within 30 million cores of the new generation of sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.

Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density functional theory (DFT) in physics are proved to be time-consuming for predicting large number of molecules. Recently, the machine learning methods, which consider much rule-based information, have also shown potentials for this issue. However, the complex inherent quantum interactions of molecules are still largely underexplored by existing solutions. In this paper, we propose a generalizable and transferable Multilevel Graph Convolutional neural Network (MGCN) for molecular property prediction. Specifically, we represent each molecule as a graph to preserve its internal structure. Moreover, the well-designed hierarchical graph neural network directly extracts features from the conformation and spatial information followed by the multilevel interactions. As a consequence, the multilevel overall representations can be utilized to make the prediction. Extensive experiments on both datasets of equilibrium and off-equilibrium molecules demonstrate the effectiveness of our model. Furthermore, the detailed results also prove that MGCN is generalizable and transferable for the prediction.

The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations of these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm for simulating frustrated magnetic systems and other strongly correlated quantum many-body systems. PEPS++ can accurately solve these models at the extreme scale with low cost and high scalability on modern heterogeneous supercomputers. We implement PEPS++ on Sunway TaihuLight based on a carefully designed tensor computation library for manipulating high-rank tensors and optimize it by invoking various high-performance matrix and tensor operations. By solving a 2D strongly frustrated$J_1$-$J_2$model with over ten million cores, PEPS++ demonstrates the capability of simulating strongly correlated quantum many-body problems at unprecedented scales with accuracy and time-to-solution far beyond the previous state of the art.

Objective: The purpose of this study is to evaluate clinical outcomes of Acupoints of Neiguan (PC6) combined with medius haemospasia in neck type cervical spondylosis (type of qistagnation and blood stasis) treatment. Method: 60 inclusive patients were randomly divided into two groups with ratio 1:1, observation group was given Acupoints of Neiguan (PC6) combined with medius haemospasia, control group was given routine acupuncture. To observe changes of patients' pain and living ability before treatment, 1 week after, 2 weeks after and 1 month after treatment. Results: 1> There were significant differences (PBoth therapies got good clinical curative effect in treatment of neck type cervical spondylosis (type of qistagnation and blood stasis). 2> Acupoints of Neiguan (PC6) combined with medius haemospasia got the same short-term and long-term efficacy with routine acupuncture.