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In this work, we characterize the capability of artificial neural network predictive models for generalizable turbulence forecasting, particularly for use in predictive adaptive optics (AO) applications. Predictive AO control, which utilizes future state predictions of an optical wavefront propagated through a turbulent medium to drive correction, is a promising technology for optical propagation in high-disturbance and low-signal environments. The dynamics describing the evolution of turbulent flow can vary greatly. Accordingly, a generalizable approach to turbulence forecasting has key benefits in allowing for prediction across a range of conditions, thus enabling continuous predictive AO operation in dynamic environments and having reduced sensitivity to changes in conditions. We present a model for generalizable turbulence forecasting, which demonstrated consistent high performance over a range of compressible flow conditions outside those included in the training sample, with only a minimal increase in prediction error compared with a hypothetical baseline model, which assumes perfect a priori characterization. These results demonstrate a clear ability to extract useful dynamics from a limited domain of turbulent conditions and apply these appropriately for forecasting, which could inform future design of predictive AO systems.