Machine learning emulators of dynamical systems for understanding ecosystem behaviour

Minimal models (MM) aim to capture the simplified behaviour of complex systems to facilitate system-level analyses that would be unfeasible with more sophisticated numerical models. However, the choices involved in minimal model development heavily rely on expert knowledge, a source of bias that can interfere with good modelling practices. In this paper, a new method is proposed in which a machine learning (ML) model is trained with transient data generated by a detailed physically-based numerical model, predicting the rate of change of the target state variables given their current value and additional drivers. The trained model is then used to mimic the analysis made with traditional minimal models. This approach (ML-MM) is deployed in a semiarid hillslope ecosystem characterising its soil and vegetation components. The ML-MM outputs share most of the general features with previous expert-based results but show a better ability of the hillslope to (1) recover its vegetation, (2) resist total disappearance of the soil and (3) reach substantially higher soil depths in steady state. Furthermore, a new intermediate stable equilibrium is found between the already known healthy and degraded ones, revealing a more complex pattern of ecosystem collapse that avoids a critical shift, as supported by numerical model simulations. The transient behaviour is also investigated, from which we conclude that the system can exhibit strong reactivity, that is, an initial deviation away from equilibrium after a perturbation. In conclusion, the present study demonstrates the potential of ML-MM to obtain new scientific insights on complex systems that might be missed by expert-based alternatives. Hence, minimal models may benefit greatly from incorporating detailed numerical models and data-driven simplification in their development process. Ultimately, this methodology could be applicable to many fields of study and even be expanded to observational data, enhancing our understanding of real-world complex system dynamics.