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A neural network (NN) model is trained with a database widely used in the aerosol remote sensing community to rapidly predict the single‐scattering optical properties of spheroidal dust particles. Analytical solutions for their Jacobians with respect to microphysical properties are derived based on the functional form of the NN. The Jacobian predictions are improved by adding Jacobians from a linearized T‐matrix model into the training. Out‐of‐database testing implies that NN‐based predictions perform better than the business‐as‐usual method that interpolates optical properties from the database. Independent validation further demonstrates the efficacy of the NN‐based predictions by reducing computational costs while maintaining accuracy. This work represents the first use of machine learning‐based function approximation to computationally expedite the application of the existing spheroidal dust properties database; the resultant NN model can be implemented in atmospheric models and satellite retrieval algorithms with high accuracy, computational efficiency, and the rigor of analytical solutions. Plain Language Summary: Dust particles affect both solar and terrestrial radiative transfer, but whether they cool or warm the climate is currently an open question in the literature. Accurate estimation of dust scattering and absorption properties, while critical for climate studies, is hindered by the fact that dust particles have irregular shapes and large size ranges; hence, no single method can be applied for all particle sizes and shapes. Often, a comprehensive look‐up table of these properties is created by combining multiple methods. The application of such databases, however, is cumbersome and inaccurate due to the need for multi‐variable interpolation. Furthermore, the look‐up‐table approach lacks the mathematical rigor needed to determine the sensitivity (Jacobians) of the single‐scattering properties to the dust size, shape, and refractive index that are needed in remote sensing algorithms. The aforementioned challenges are tackled here by developing a novel approach within the neural network (NN) framework. This NN‐based approach is fast, accurate, and able to predict Jacobians with analytical formulas. The NN model can be readily applied to the dust retrieval algorithm and radiative forcing modeling. The concept of deriving Jacobians from the NN model in this study can also be generalized for application to other problems involving gradient calculations. Key Points: A neural network (NN) model is trained to characterize the optical properties of spheroidal dust particlesAnalytical Jacobians of the optical properties with respect to microphysical parameters are derived from NN model directlyAdding analytical Jacobians from a linearized T‐matrix model in the training improves the NN‐derived Jacobians [ABSTRACT FROM AUTHOR]