Multi-agent models are widely used across the quantitative sciences to analyse complex systems. These often contain parameters (ranging from a handful of SDE parameters to entire graph adjacency matrices) which must be estimated from data. While many methods to do so have been developed, they can be mathematically involved, computationally expensive, or unable to deal with non-unique inference problems. We present an alternative using neural networks that addresses all these issues. The use of neural networks allows for uncertainty quantification in a manner that reflects both the noise on the data as well as the non-convexity of the parameter estimation problem. We discuss applications to various different examples, including learning SDE parameters for the SIR model of epidemics, estimating the location of power line failures in the British transmission grid, or learning connectivity matrices for the flow of supply and demand across Greater London, and give a comparative analysis of our method’s performance in terms of speed, prediction accuracy, and uncertainty quantification. Our method can make accurate predictions from various kinds of data in seconds where more classical techniques, such as MCMC, take hours, thereby presenting researchers across the quantitative disciplines with a valuable tool to estimate relevant parameters and produce more meaningful simulations at a greatly reduced computational cost.