Physics-constrained machine learning for decoding multi-nanobubble configurations in graphene
Identifying multiple graphene nanobubbles from electronic spectra is challenging because their strain-induced features overlap. We develop a physics-constrained machine-learning framework that decodes nanobubble configurations from density-of-states (DOS) spectra. For spatially separated nanobubbles, previous full quantum-transport calculations established that the multi-bubble DOS is numerically equivalent to the normalized sum of the constituent single-bubble spectra. We encode this validated additive relation in a compact neural decomposition model. For each target spectrum, the basis coefficients are optimized independently, and the resulting weights directly identify the constituent geometries. The method accurately reconstructs configurations of increasing complexity and remains robust to repeated constituents, incomplete basis dictionaries, and simulated measurement noise. The framework provides an interpretable route for characterizing strain-engineered graphene nanostructures and may extend to other quantum materials with additive spectral responses.