The ability to non-invasively measure local conductivity and permittivity at the nanoscale is of fundamental importance in unraveling the physics of quantum systems. One approach is Microwave Impedance Microscopy (MIM), a scanning probe technique operating at microwave frequencies. However, the resulting large datasets and vast parameter space make obtaining a mapping between MIM measurements and local microscopic properties challenging. Here, we overcome this challenge by using machine learning to reconstruct the local properties while incorporating physical priors. The synergy between MIM and ML allows for the quantitative predictions of complex interactions between excitons, charge carriers, and the dielectric environment. This approach provides profound insights into the fundamental physics of excitons in two-dimensional materials.