Solving sign problems with physics-informed kernels

TL;DR

This paper introduces a physics-informed kernel-based generative architecture that effectively addresses sign problems and enables efficient sampling in complex probability distributions, demonstrated on quantum and field theory models.

Contribution

The paper presents a novel generative architecture using physics-informed kernels that preserves probability weights and maps complex sampling tasks to sign-problem free manifolds.

Findings

Successfully applied to zero-dimensional field theories with complex couplings

Demonstrated effectiveness in real-time quantum harmonic oscillator evolution

Achieved efficient sampling and sign problem resolution

Abstract

In the present work we construct a novel generative architecture for systems with complex probability distributions. In general, these sampling tasks come with two challenges: resolving sign problems and efficient sampling. The architecture is based on physics-informed kernels (PIKs) introduced in arXiv:2510.26678, and aims at resolving both challenges. Key to the complex PIK-architecture is its probability-weight preserving property, which allows us to map the sampling task to one on a sign-problem free manifold with a simple distribution and efficient sampling. The potential of this novel architecture is demonstrated within applications to zero-dimensional field theories with complex couplings, as well as the real-time evolution of the quantum-mechanical harmonic oscillator.