An established model for sound energy decay functions (EDFs) is the superposition of multiple exponentials and a noise term. This work proposes a neural-network-based approach for estimating the model parameters from EDFs. The network is trained on synthetic EDFs and evaluated on two large datasets of over 20000 EDF measurements conducted in various acoustic environments. The evaluation shows that the proposed neural network architecture robustly estimates the model parameters from large datasets of measured EDFs, while being lightweight and computationally efficient. An implementation of the proposed neural network is publicly available.