A quatum inspired neural network for geometric modeling

• DOI: 10.48550/arxiv.2401.01801
• Publication Date: 2024-01-01
• Authors: Weitao Du; Shengchao Liu; Hongyu Guo

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make them adept at modeling molecules and crystalline materials. However, current GNNs only offer a mean-field approximation of the system, encapsulated within two-body message passing, thus falling short in capturing intricate relationships these graphs. To address this limitation, tensor networks, widely employed by computational physics to handle manybody using high-order tensors, been introduced. Nevertheless, integrating tensorized into framework faces scalability symmetry conservation (e.g., permutation rotation) challenges. response, we introduce an innovative equivariant Matrix Product State (MPS)-based strategy, through achieving efficient implementation contraction operation. Our method effectively models complex relationships, suppressing approximations, captures symmetries Importantly, it seamlessly replaces standard layer-aggregation modules intrinsic GNNs. We empirically validate superior accuracy our approach on benchmark tasks, including predicting classical Newton quantum Hamiltonian matrices. knowledge, represents inaugural utilization parameterized networks.