A Survey of Neural Network Variational Monte Carlo from a Computing Workload Characterization Perspective

TL;DR

This paper surveys and empirically characterizes the GPU workload of Neural Network Variational Monte Carlo methods, revealing bottlenecks and guiding optimization strategies for scalable quantum many-body problem solutions.

Contribution

It provides a workload-oriented GPU profiling and analysis of NNVMC, highlighting performance bottlenecks and suggesting hardware-aware optimization approaches.

Findings

End-to-end performance limited by low-intensity kernels

Kernel behavior varies across ans"atze and stages

Memory and compute balance differ significantly

Abstract

Neural Network Variational Monte Carlo (NNVMC) has emerged as a promising paradigm for solving quantum many-body problems by combining variational Monte Carlo with expressive neural-network wave-function ans\"atze. Although NNVMC can achieve competitive accuracy with favorable asymptotic scaling, practical deployment remains limited by high runtime and memory cost on modern graphics processing units (GPUs). Compared with language and vision workloads, NNVMC execution is shaped by physics-specific stages, including Markov-Chain Monte Carlo sampling, wave-function construction, and derivative/Laplacian evaluation, which produce heterogeneous kernel behavior and nontrivial bottlenecks. This paper provides a workload-oriented survey and empirical GPU characterization of four representative ans\"atze: PauliNet, FermiNet, Psiformer, and Orbformer. Using a unified profiling protocol, we analyze model-level runtime and memory trends and kernel-level behavior through family breakdown, arithmetic intensity, roofline positioning, and hardware utilization counters. The results show that end-to-end performance is often constrained by low-intensity elementwise and data-movement kernels, while the compute/memory balance varies substantially across ans\"atze and stages. Based on these findings, we discuss algorithm--hardware co-design implications for scalable NNVMC systems, including phase-aware scheduling, memory-centric optimization, and heterogeneous acceleration.