Data-driven modeling of Galactic diffuse emission with multi-wavelength observations

Abstract We present a data-driven investigation of Galactic diffuse emission. Using multi-frequency Planck maps (30–857 GHz), we construct a non-linear mapping between microwave-to-far-infrared and gamma-ray intensity through supervised machine learning. Our models achieve high predictive accuracy ( $$R^2>$$ R 2 > 0.90 in the 0.1–10 GeV range), demonstrating that multi-band Planck emission encodes sufficient information to reconstruct both spatial morphology and spectral properties of diffuse gamma-ray emission. By analyzing model performance across different frequency bands and spatial regions, we find that the high-frequency Planck bands are the dominant predictors, indicating that the learned mapping is primarily driven by gas- and dust-correlated structures encoded in the adopted interstellar emission model. Above 10 GeV, the increasing relevance of the low-frequency bands is consistent with synchrotron-traced cosmic-ray electron structures that may be associated with leptonic inverse Compton emission. Residual maps reveal coherent large-scale structures, including Loop I and III, highlighting regions where standard interstellar emission models are incomplete or biased. Compared with the GALPROP model, our machine learning approach yields a higher $$R^2=0.95$$ R 2 = 0.95 and lower mean absolute relative error (14.7%) in the inner Galactic disk and the Galactic Center (GC) region at $$\sim $$ ∼ 4.3 GeV. Our results illustrate that machine learning serves as a physically interpretable tool for multi-messenger astrophysics, providing a data-driven baseline for separating non-standard emission components and deriving new constraints on cosmic-ray propagation and interstellar medium structure.