Aerosols influence Earth's radiative balance via the scattering and absorbing of solar radiation, affect cloud formation, and play important roles on precipitation, ocean seeding and human health. Accurate modeling of these effects requires knowledge of the the chemical composition and size distribution of aerosol particles present in the atmosphere. Computationally intensive applications like remote sensing and weather forecasting commonly use simplified representations of aerosol microphysics, prescribing the aerosol size distribution (ASD), introducing uncertainty in climate predictions and aerosol retrievals. This work develops a neural network model, termed MAMnet, to predict the ASD and mixing state using the bulk mass of aerosol and the meteorological state. MAMnet can be driven by the output of single moment, mass-based, aerosol schemes or using reanalysis products. We show that MAMnet is able to accurately reproduce the predictions of a two-moment microphysics aerosol model as well as field measurements. Our model paves the way to improve the physical representation of aerosols in physical models while maintaining the versatility and efficiency required in large scale applications.