We present a simple and scalable implementation of next-generation reservoir computing for modeling dynamical systems from time series data. Our approach uses a pseudorandom nonlinear projection of time-delay embedded input, allowing an arbitrary dimension of the feature space, thus providing a flexible alternative to the polynomial-based projections used in previous next-generation reservoir computing variants. We apply the method to benchmark tasks -- including attractor reconstruction and bifurcation diagram estimation -- using only partial and noisy observations. We also include an exploratory example of estimating asymptotic oscillation phases. The models remain stable over long rollouts and generalize beyond training data. This framework enables the precise control of system state and is well suited for surrogate modeling and digital twin applications.

It has been found recently that more data can, counter-intuitively, hurt the performance of deep neural networks. Here, we show that a more extreme version of the phenomenon occurs in data-driven models of dynamical systems. To elucidate the underlying mechanism, we focus on next-generation reservoir computing (NGRC) -- a popular framework for learning dynamics from data. We find that, despite learning a better representation of the flow map with more training data, NGRC can adopt an ill-conditioned ``integrator'' and lose stability. We link this data-induced instability to the auxiliary dimensions created by the delayed states in NGRC. Based on these findings, we propose simple strategies to mitigate the instability, either by increasing regularization strength in tandem with data size, or by carefully introducing noise during training. Our results highlight the importance of proper regularization in data-driven modeling of dynamical systems.