Short communication: Learning how landscapes evolve with neural operators

Abstract. The use of Fourier Neural Operators (FNOs) to learn how landscapes evolve is introduced. The approach makes use of recent developments in deep learning to learn the processes involved in evolving landscapes (e.g., erosion). An example is provided in which FNOs are developed using input–output pairs (elevations at different times) in synthetic landscapes generated using the stream power model (SPM). The SPM takes the form of a non-linear partial differential equation that advects slopes headwards. The results indicate that the learned operators can reliably and very rapidly predict subsequent landscape evolution at large scales. These results suggest that FNOs could be used to rapidly predict landscape evolution without recourse to the (slow) computation of flow routing and time stepping needed when generating numerical solutions to the SPM. More broadly, they suggest that neural operators could be used to learn the processes that evolve actual and analogue landscapes. Interesting future work could involve assessment of whether learned operators can be applied to other settings or model parametrizations.