Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator

Analog quantum simulators provide access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data is often hindered by measurement noise, limited observables, and incomplete knowledge of the underlying microscopic model. Here, we develop a machine learning approach based on a variational autoencoder (VAE) to analyze interference measurements of tunnel-coupled one-dimensional Bose gases, which realize the sine-Gordon quantum field theory. Trained in an unsupervised manner, the VAE learns a minimal latent representation that strongly correlates with the equilibrium control parameter of the system. Applied to non-equilibrium protocols, the latent space uncovers signatures of frozen-in solitons following rapid cooling, and reveals anomalous post-quench dynamics not captured by conventional correlation-based methods. These results demonstrate that generative models can extract physically interpretable variables directly from noisy and sparse experimental data, providing complementary probes of equilibrium and non-equilibrium physics in quantum simulators. More broadly, our work highlights how machine learning can supplement established field-theoretical techniques, paving the way for scalable, data-driven discovery in quantum many-body systems.