Simulating the evolution of a coagulating aerosol or cloud of droplets in a key problem in atmospheric science. We present a proof of concept for modeling coagulation processes using a novel combinatorally-invariant neural network (CiNN) architecture. Using two types of data from a high-detail particle-resolved aerosol simulation, we show that CiNN models outperform standard neural networks and are competitive in accuracy with traditional stateof-the-art sectional models. These CiNN models could have application in learning coarsegrained coagulation models for multi-species aerosols and for learning coagulation models from observed size-distribution data.