arXiv subjects

An-Jun Liu

Publications and source records attributed to An-Jun Liu.

3 recordsLinked to original sources

arXiv2026

Neural network backflow for ab-initio solid calculations

Accurately simulating extended periodic systems is a central challenge in condensed matter physics. Neural quantum states (NQS) offer expressive wavefunctions for this task but face issues with scalability. In this work, we successfully extend the neural network backflow (NNBF) approach to ab-initio solid-state materials. Building on our scalable optimization framework for molecules [Liu et al., PRB 112, 155162 (2025)], we introduce a two-stage pruning strategy to manage the massive configuration space expansions: by utilizing a computationally cheap, physics-informed importance proxy, we devote exact NNBF amplitude evaluations solely to the most relevant determinants, significantly improving optimization efficiency, energy estimation, and convergence. Our framework achieves state-of-the-art accuracy across diverse solid-state benchmarks. For 1D hydrogen chains, NNBF matches or surpasses DMRG and AFQMC, remains robust in strongly correlated bond-breaking regimes where coupled-cluster methods fail, and smoothly extrapolates to the thermodynamic limit. We further demonstrate its scalability by computing ground-state potential energy curves for 2D graphene and 3D silicon. Finally, ablation studies validate the computational savings of our pruning strategy and highlight the dependence of the NNBF energies on basis sets.

cond-mat.str-el↗

arXiv2025

Efficient optimization of neural network backflow for ab-initio quantum chemistry

The ground state of second-quantized quantum chemistry Hamiltonians is key to determining molecular properties. Neural quantum states (NQS) offer flexible and expressive wavefunction ansatze for this task but face two main challenges: highly peaked ground-state wavefunctions hinder efficient sampling, and local energy evaluations scale quartically with system size, incurring significant computational costs. In this work, we overcome these challenges by introducing a suite of algorithmic enhancements, which includes efficient periodic compact subspace construction, truncated local energy evaluations, improved stochastic sampling, and physics-informed modifications. Applying these techniques to the neural network backflow (NNBF) ansatz, we demonstrate significant gains in both accuracy and scalability. Our enhanced method surpasses traditional quantum chemistry methods like CCSD and CCSD(T), outperforms other NQS approaches, and achieves competitive energies with state-of-the-art ab initio techniques such as HCI, ASCI, FCIQMC, and DMRG. A series of ablation and comparative studies quantifies the contribution of each enhancement to the observed improvements in accuracy and efficiency. Furthermore, we investigate the representational capacity of the ansatz, finding that its performance correlates with the inverse participation ratio (IPR), with more delocalized states being more challenging to approximate.

physics.chem-ph↗

arXiv2024

Neural network backflow for ab-initio quantum chemistry

The ground state of second-quantized quantum chemistry Hamiltonians provides access to an important set of chemical properties. Wavefunctions based on ML architectures have shown promise in approximating these ground states in a variety of physical systems. In this work, we show how to achieve state-of-the-art energies for molecular Hamiltonians using the the neural network backflow wave-function. To accomplish this, we optimize this ansatz with a variant of the deterministic optimization scheme based on SCI introduced by [Li, et. al JCTC (2023)] which we find works better than standard MCMC sampling. For the molecules we studied, NNBF gives lower energy states than both CCSD and other neural network quantum states. We systematically explore the role of network size as well as optimization parameters in improving the energy. We find that while the number of hidden layers and determinants play a minor role in improving the energy, there is significant improvements in the energy from increasing the number of hidden units as well as the batch size used in optimization with the batch size playing a more important role.

physics.chem-ph↗