The atomistic Hubbard interaction $U$, representing the on-site Coulomb repulsion, serves as a pivotal parameter in theoretical models describing correlated systems, yet its precise experimental determination, especially in moiré systems, remains challenging. Scanning tunneling microscopy (STM) provides real-space images of the local density of states (LDOS), offering rich datasets that reflect the unique electronic structure of the material. Here, we introduce a systematic methodology for extracting the Hubbard $U$ parameter directly from these LDOS images through the application of machine learning in the case of twisted bilayer graphene in the flat-band regime. Accurate regression of $U$ is achieved despite the extremely high visual similarity between Fourier transform-LDOS (FT-LDOS) images corresponding to different interaction strengths. Subsequent data analysis further suggests a gradual interaction-dependent redistribution of spectral weight, with a possible crossover scale of order $U/t\sim 1$. To assess robustness beyond idealized simulations, we introduce physically motivated perturbations that emulate experimental STM imperfections and demonstrate that augmentation-based training substantially improves generalization to noisy and symmetry-broken FT-LDOS images.

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• Inverse problems
• Local density of states
• Twisted bilayer graphene
• Convolutional neural networks
• Hubbard model
• Machine learning
• Scanning tunneling microscopy