Machine Learning Prediction of Magnetic Proximity Effect in van der Waals Heterostructures: From Atoms to Moiré

We introduce a machine learning framework that efficiently predicts large-scale proximity-induced magnetism in van der Waals heterostructures, overcoming the high computational cost of density functional theory (DFT). We apply it to graphene/\CGT, which exhibits a previously unrecognized dichotomy. Unlike the spin polarization at the Fermi level, which follows the pseudospin, the proximity-induced magnetic moments vary across carbon atoms, defying analytical modeling. To address this, we develop an ensemble-based regression model trained on DFT data and employ local environment descriptors to map the local ($\sim 2$,nm${}^2$) atomic-scale geometry to the carbon magnetic moments. Besides demonstrating locality, the model reveals rich magnetic moiré textures. Crucially, this method can be broadly applied to orbital and spin proximity effects that are highly sensitive to local atomic environments and are beyond analytical description.