Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time $10^3-10^4$ times faster for training process and training data set $\sim 10^2$ times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational cost and training data, each by a factor of $\sim$10.