Diffusion Models as Stochastic Quantization in Lattice Field Theory
In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional $\phi^4$ theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.
Code (1)
Tasks
QuantizationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Generative Diffusion Models for Lattice Field Theory
This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We s…
QuantizationPhysics-Conditioned Diffusion Models for Lattice Gauge Theory
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to …
QuantizationReaction-diffusion kinetics on lattice at the microscopic scale
Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spa…
Machine learning for four-dimensional SU(3) lattice gauge theories
In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap\-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applica…
Group-Equivariant Diffusion Models for Lattice Field Theory
Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetr…