Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems

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.

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.

\underline{E2}Former: A Linear-time \underline{E}fficient and \underline{E}quivariant Trans\underline{former} for Scalable Molecular Modeling

Equivariant Graph Neural Networks (EGNNs) have demonstrated significant success in modeling microscale systems, including those in chemistry, biology and materials science. However, EGNNs face substantial computational challenges due to the high cost of constructing edge features via spherical tensor products, making them impractical for large-scale systems. To address this limitation, we introduce E2Former, an equivariant and efficient transformer architecture that incorporates the Wigner $6j$ convolution (Wigner $6j$ Conv). By shifting the computational burden from edges to nodes, the Wigner $6j$ Conv reduces the complexity from $O(|\mathcal{E}|)$ to $ O(| \mathcal{V}|)$ while preserving both the model's expressive power and rotational equivariance. We show that this approach achieves a 7x-30x speedup compared to conventional $\mathrm{SO}(3)$ convolutions. Furthermore, our empirical results demonstrate that the derived E2Former mitigates the computational challenges of existing approaches without compromising the ability to capture detailed geometric information. This development could suggest a promising direction for scalable and efficient molecular modeling.

A Survey of Generative AI for De Novo Drug Design: New Frontiers in Molecule and Protein Generation

Artificial intelligence (AI)-driven methods can vastly improve the historically costly drug design process, with various generative models already in widespread use. Generative models for de novo drug design, in particular, focus on the creation of novel biological compounds entirely from scratch, representing a promising future direction. Rapid development in the field, combined with the inherent complexity of the drug design process, creates a difficult landscape for new researchers to enter. In this survey, we organize de novo drug design into two overarching themes: small molecule and protein generation. Within each theme, we identify a variety of subtasks and applications, highlighting important datasets, benchmarks, and model architectures and comparing the performance of top models. We take a broad approach to AI-driven drug design, allowing for both micro-level comparisons of various methods within each subtask and macro-level observations across different fields. We discuss parallel challenges and approaches between the two applications and highlight future directions for AI-driven de novo drug design as a whole. An organized repository of all covered sources is available at https://github.com/gersteinlab/GenAI4Drug.