  We develop a generative neural network for the generation of sparse data in
particle physics using a permutation-invariant and physics-informed loss
function. The input dataset used in this study consists of the particle
constituents of hadronic jets due to its sparsity and the possibility of
evaluating the network's ability to accurately describe the particles and jets
properties. A variational autoencoder composed of convolutional layers in the
encoder and decoder is used as the generator. The loss function consists of a
reconstruction error term and the Kullback-Leibler divergence between the
output of the encoder and the latent vector variables. The
permutation-invariant loss on the particles' properties is combined with two
mean-squared error terms that measure the difference between input and output
jets mass and transverse momentum, which improves the network's generation
capability as it imposes physics constraints, allowing the model to learn the
kinematics of the jets.
