Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this domain, their substantial computational cost-driven by high-order tensor product (TP) operations-restricts their scalability to large molecular systems with extensive basis sets. To address this challenge, we introduce SPHNet, an efficient and scalable equivariant network that incorporates adaptive sparsity into Hamiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations, significantly reducing tensor product computations while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70 percent. Extensive evaluations on QH9 and PubchemQH datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact.

scDiffusion: conditional generation of high-quality single-cell data using diffusion model

Single-cell RNA sequencing (scRNA-seq) data are important for studying the biology of development or diseases at single-cell level. To better understand the properties of the data, to build controlled benchmark data for testing downstream methods, and to augment data when collecting sufficient real data is challenging, generative models have been proposed to computationally generate synthetic scRNA-seq data. However, the data generated with current models are not very realistic yet, especially when we need to generate data with controlled conditions. In the meantime, the Diffusion models have shown their power in generating data in computer vision at high fidelity, providing a new opportunity for scRNA-seq generation. In this study, we developed scDiffusion, a diffusion-based model to generate high-quality scRNA-seq data with controlled conditions. We designed multiple classifiers to guide the diffusion process simultaneously, enabling scDiffusion to generate data under multiple condition combinations. We also proposed a new control strategy called Gradient Interpolation. This strategy allows the model to generate continuous trajectories of cell development from a given cell state. Experiments showed that scDiffusion can generate single-cell gene expression data closely resembling real scRNA-seq data, surpassing state-of-the-art models in multiple metrics. Also, scDiffusion can conditionally produce data on specific cell types including rare cell types. Furthermore, we could use the multiple-condition generation of scDiffusion to generate cell type that was out of the training data. Leveraging the Gradient Interpolation strategy, we generated a continuous developmental trajectory of mouse embryonic cells. These experiments demonstrate that scDiffusion is a powerful tool for augmenting the real scRNA-seq data and can provide insights into cell fate research.