Technical Note: Deep-GF-PRM – A physics-informed deep learning framework for parameterizing aerosol hygroscopic growth factor probability density function

Abstract. The hygroscopic properties of atmospheric aerosols are crucial for quantifying their impact on radiation and cloud formation. They are often characterized by a growth factor probability density function (GF-PDF), which can be parameterized as a superposition of multiple Gaussian distributions. Conventionally, nonparametric inversion methods are developed to retrieve GF-PDF from the instrument responses, e.g., measurements of humidified tandem differential mobility analyzer. However, additional parametric fittings are required to extract modal parameters from the inverted GF-PDF, a process that is computationally intensive and susceptible to fitting errors.

In this study, we introduce Deep-GF-PRM, a deep learning framework that parameterizes the GF-PDF modal parameters directly from the instrument responses. The core of Deep-GF-PRM is a physics-informed neural network that embeds the instrument’s kernel function and physical constraints, creating end-to-end mapping of the GF-PDF modal parameters to the instrument response. Trained on a large dataset of synthetic instrument responses generated using a wide range of GF-PDFs and noise levels, Deep-GF-PRM accurately reproduces synthetic GF-PDFs and retrieves modal parameters with higher fidelity than conventional fitting approaches. The model is applied to real-world measurements, and yields results highly consistent with nonparametric inversions. Deep-GF-PRM thus provides an efficient and unsupervised solution for parameterizing aerosol hygroscopic properties.