Prediction of the atomistic Hubbard U interaction from moir\'e system STM-images using image recognition

The atomistic Hubbard interaction U, representing the on-site Coulomb repulsion, serves as a pivotal parameter in theoretical models describing of correlated systems, yet its precise experimental determination especially in moir\'e systems remains challenging. Scanning Tunneling Microscopy(STM) provides real-space images of the local density of states (LDOS), offering rich data sets 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 (ML) in the case of twisted bilayer graphene in the flat-band regime. The regression of U is highly accurate even though the image-similarity is greater than 99.98%. Subsequent data-analysis further suggest a weak crossover between the weak and strong coupling regime at Uc/t 1