Toward Scalable Normalizing Flows for the Hubbard Model

2026-01-26

AI Summary

This work investigates the effective scaling of normalizing flows to larger lattice sizes and lower temperatures in the Hubbard model for efficient learning of its Boltzmann distribution. Addressing the scalability bottleneck of normalizing flows in strongly correlated fermionic systems, we integrate stochastic normalizing flows with nonequilibrium Markov chain Monte Carlo (MCMC) methods, systematically analyzing their stability, computational efficiency, and resource requirements in the low-temperature, large-scale limit. Our study is the first to reveal the scaling behavior of normalizing flows under these challenging conditions and establishes a stable, scalable pathway for generative modeling of strongly correlated quantum systems.

Technology Category

• Machine Learning: Scalability of ML Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. Additionally, we present the scaling behavior of stochastic normalizing flows and non-equilibrium Markov chain Monte Carlo methods for this fermionic system.

Problem

• normalizing flows
• Hubbard model
• scalability
• low temperature
• large lattice size

Innovation

• normalizing flows
• Hubbard model
• scalability
• non-equilibrium MCMC
• stochastic normalizing flows