Sparse identification of non-linear dynamics (SINDy) of landscape evolution model simulations

Abstract

This study, titled "Sparse Identification of Nonlinear Dynamics (SINDy) of Landscape Evolution Model (LEM) Simulations" explores the linear inference of differential physical processes simulated by the LEM called Landlab by using the SINDy toolkit. The research aims to enable LEM researchers to incorporate data trained models to explain nonlinear phenomena alongside the traditional approach of physical equations. The study employed an iterative approach to investigate explanation of the non-linear Taylor diffusion process from simulation data using a sparse, linear model. The data was collected from the simulations run by the LEM model Landlab which incorporated a non-linear hillslope and a fluvial flux process. Results suggest that the underlying nonlinear dynamic could be identified with a trained SINDy model in a relatively sparse manner with a median average percentage error as low as 0.097%. Although, the simulations ran with the trained model exhibited drift from the original course of model data. This is expected due to stochasticity of non-linear models. The findings of this study reveal that soil elevation at a node in a spatial grid can be inferred using the elevation values of the neighboring nodes as model features. This has important implications for LEM modelling providing viable employable alternatives to representative physical equations. Additionally, this study contributes to the existing body of knowledge in earth sciences by showing that it is possible to linearize a process in spatial domain simulations when treated as a dynamical system. Furthermore, the study highlights the challenge of reducing number of terms in a linear model to just a few, which can contribute to further research in this area. In conclusion, this study sheds light on treating differential physical processes in a spatial domain as sparse linear models and providing valuable insights for researchers who design or employ LEM's in their studies.