Numerical modeling of non-inertial particles dynamics is usually addressed by solving a population balance equation (PBE). In addition to space and time, a discretization is required also in the particle-size space, which can cover a large range of variation controlled by strongly nonlinear phenomena. A novel approach is presented in which a hybrid stochastic/fixed-sectional method solving the PBE is used to train a combination of an artificial neural network (ANN) with a convolutional neural network (CNN) and recurrent long short-term memory artificial neural layers (LSTM), to predict the time evolution of the PBE. Instead of solving directly for the particle number density over sections, the hybrid stochastic/fixed-sectional method decomposes the problem into the total number density and the probability density function (PDF) of sizes, allowing for an accurate treatment of surface growth/loss with a Monte Carlo method for training the neural networks. The input of the ANN is composed of the thermochemical parameters controlling the physics of nucleation, surface growth/loss and agglomeration/coagulation of the particles. The input of the CNN is the shape of the particle size distribution (PSD) discretized in sections of size. From these inputs, in a flow simulation the ANN-CNN returns the PSD shape for the subsequent time step or a source term for the Eulerian transport of the particle size density. The method is first evaluated in a canonical laminar premixed sooting flame of the literature and for a given level of accuracy, a significant computing cost reduction is achieved (6 times faster compared to a sectional method with 10 sections and 30 times faster for 100 sections). Then, this novel methodology is applied to predict the particulate emissions from an aircraft engine combustion chamber.