Title: An Optimally Weighted Echo State Neural Network for Highly Chaotic Time Series Modelling. Abstract: We demonstrate the development and implementation of a series of echo state neural networks in conjunction with optimal weighted averaging to produce robust, model-free predictions of highly chaotic time series. We deploy our model on simulated mass accretion data sets governing the formation of a protostar, accretion disk and gas envelope. Our methodology extends the parallel series approach of averaging all reservoir outputs by instead selecting an optimal set of weights for each realization representative of what we believe constructs the optimal output signal that best represents the data’s underlying temporal dynamics. The method is demonstrated by modelling hydrodynamic and stellar evolution simulations that are representative of highly chaotic systems.