Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is frequently limited by the substantial computational resources required to construct the Kohn-Sham Hamiltonian. In response to these limitations, current research has employed deep-learning models to efficiently predict molecular and solid Hamiltonians, with roto-translational symmetries encoded in their neural networks. However, the scalability of prior models may be problematic when applied to large molecules, resulting in non-physical predictions of ground-state properties. In this study, we generate a substantially larger training set (PubChemQH) than used previously and use it to create a scalable model for DFT calculations with physical accuracy. For our model, we introduce a loss function derived from physical principles, which we call Wavefunction Alignment Loss (WALoss). WALoss involves performing a basis change on the predicted Hamiltonian to align it with the observed one; thus, the resulting differences can serve as a surrogate for orbital energy differences, allowing models to make better predictions for molecular orbitals and total energies than previously possible. WALoss also substantially accelerates self-consistent-field (SCF) DFT calculations. Here, we show it achieves a reduction in total energy prediction error by a factor of 1347 and an SCF calculation speed-up by a factor of 18%. These substantial improvements set new benchmarks for achieving accurate and applicable predictions in larger molecular systems.

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.

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this challenge, we introduce Neural P$^3$M, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner. Neural P$^3$M exhibits flexibility across a wide range of molecular systems and demonstrates remarkable accuracy in predicting energies and forces, outperforming on benchmarks such as the MD22 dataset. It also achieves an average improvement of 22% on the OE62 dataset while integrating with various architectures.

In this study, we introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model, which incorporates Deep Equilibrium Models (DEQs) for predicting Density Functional Theory (DFT) Hamiltonians. The DEQH model inherently captures the self-consistency nature of Hamiltonian, a critical aspect often overlooked by traditional machine learning approaches for Hamiltonian prediction. By employing DEQ within our model architecture, we circumvent the need for DFT calculations during the training phase to introduce the Hamiltonian's self-consistency, thus addressing computational bottlenecks associated with large or complex systems. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians. When benchmarked on the MD17 and QH9 datasets, DE-QHNet, an instantiation of the DEQH framework, has demonstrated a significant improvement in prediction accuracy. Beyond a predictor, the DEQH model is a Hamiltonian solver, in the sense that it uses the fixed-point solving capability of the deep equilibrium model to iteratively solve for the Hamiltonian.

Predicting the mean-field Hamiltonian matrix in density functional theory is a fundamental formulation to leverage machine learning for solving molecular science problems. Yet, its applicability is limited by insufficient labeled data for training. In this work, we highlight that Hamiltonian prediction possesses a self-consistency principle, based on which we propose self-consistency training, an exact training method that does not require labeled data. It distinguishes the task from predicting other molecular properties by the following benefits: (1) it enables the model to be trained on a large amount of unlabeled data, hence addresses the data scarcity challenge and enhances generalization; (2) it is more efficient than running DFT to generate labels for supervised training, since it amortizes DFT calculation over a set of queries. We empirically demonstrate the better generalization in data-scarce and out-of-distribution scenarios, and the better efficiency over DFT labeling. These benefits push forward the applicability of Hamiltonian prediction to an ever-larger scale.

In this paper, we develop SE3Set, an SE(3) equivariant hypergraph neural network architecture tailored for advanced molecular representation learning. Hypergraphs are not merely an extension of traditional graphs; they are pivotal for modeling high-order relationships, a capability that conventional equivariant graph-based methods lack due to their inherent limitations in representing intricate many-body interactions. To achieve this, we first construct hypergraphs via proposing a new fragmentation method that considers both chemical and three-dimensional spatial information of molecular system. We then design SE3Set, which incorporates equivariance into the hypergragh neural network. This ensures that the learned molecular representations are invariant to spatial transformations, thereby providing robustness essential for accurate prediction of molecular properties. SE3Set has shown performance on par with state-of-the-art (SOTA) models for small molecule datasets like QM9 and MD17. It excels on the MD22 dataset, achieving a notable improvement of approximately 20% in accuracy across all molecules, which highlights the prevalence of complex many-body interactions in larger molecules. This exceptional performance of SE3Set across diverse molecular structures underscores its transformative potential in computational chemistry, offering a route to more accurate and physically nuanced modeling.

Molecular dynamics (MD) is a crucial technique for simulating biological systems, enabling the exploration of their dynamic nature and fostering an understanding of their functions and properties. To address exploration inefficiency, emerging enhanced sampling approaches like coarse-graining (CG) and generative models have been employed. In this work, we propose a \underline{Frame-to-Frame} generative model with guided \underline{Flow}-matching (F$3$low) for enhanced sampling, which (a) extends the domain of CG modeling to the SE(3) Riemannian manifold; (b) retreating CGMD simulations as autoregressively sampling guided by the former frame via flow-matching models; (c) targets the protein backbone, offering improved insights into secondary structure formation and intricate folding pathways. Compared to previous methods, F$3$low allows for broader exploration of conformational space. The ability to rapidly generate diverse conformations via force-free generative paradigm on SE(3) paves the way toward efficient enhanced sampling methods.

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. In this work, we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep-learning functional model. We build the essential nonlocality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those in training, which unleashes the appealing scaling for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

In the technical report, we provide our solution for OGB-LSC 2022 Graph Regression Task. The target of this task is to predict the quantum chemical property, HOMO-LUMO gap for a given molecule on PCQM4Mv2 dataset. In the competition, we designed two kinds of models: Transformer-M-ViSNet which is an geometry-enhanced graph neural network for fully connected molecular graphs and Pretrained-3D-ViSNet which is a pretrained ViSNet by distilling geomeotric information from optimized structures. With an ensemble of 22 models, ViSNet Team achieved the MAE of 0.0723 eV on the test-challenge set, dramatically reducing the error by 39.75% compared with the best method in the last year competition.

Understanding protein sequences is vital and urgent for biology, healthcare, and medicine. Labeling approaches are expensive yet time-consuming, while the amount of unlabeled data is increasing quite faster than that of the labeled data due to low-cost, high-throughput sequencing methods. In order to extract knowledge from these unlabeled data, representation learning is of significant value for protein-related tasks and has great potential for helping us learn more about protein functions and structures. The key problem in the protein sequence representation learning is to capture the co-evolutionary information reflected by the inter-residue co-variation in the sequences. Instead of leveraging multiple sequence alignment as is usually done, we propose a novel method to capture this information directly by pre-training via a dedicated language model, i.e., Pairwise Masked Language Model (PMLM). In a conventional masked language model, the masked tokens are modeled by conditioning on the unmasked tokens only, but processed independently to each other. However, our proposed PMLM takes the dependency among masked tokens into consideration, i.e., the probability of a token pair is not equal to the product of the probability of the two tokens. By applying this model, the pre-trained encoder is able to generate a better representation for protein sequences. Our result shows that the proposed method can effectively capture the inter-residue correlations and improves the performance of contact prediction by up to 9% compared to the MLM baseline under the same setting. The proposed model also significantly outperforms the MSA baseline by more than 7% on the TAPE contact prediction benchmark when pre-trained on a subset of the sequence database which the MSA is generated from, revealing the potential of the sequence pre-training method to surpass MSA based methods in general.