Hybrid Modelling: Bridging Neural Networks and Physics-Based Approaches in Terrestrial Biogeochemical Ecosystems

The application of automatic differentiation and deep learning approaches to tackle current challenges is now a widespread practice. The biogeosciences community is no stranger to this trend; however, quite often, previously known physical model abstractions are discarded.In this study, we model the ecosystem dynamics of vegetation, water, and carbon cycles adopting a hybrid approach. This methodology involves preserving the physical model representations for simulating the targeted processes while utilizing neural networks to learn the spatial variability of their parameters. These models have historically posed challenges due to their complex process representations, varied spatial scales, and parametrizations.We show that a hybrid approach effectively predicts model parameters with a single neural network, compared with the site-level optimized set of parameters. This approach demonstrates its capability to generate predictions consistent with in-situ parameter calibrations across various spatial locations, showcasing its versatility and reliability in modelling coupled systems.Here, the physics-based process models undergo evaluation across several FLUXNET sites. Various observationssuch as gross primary productivity, net ecosystem exchange, evapotranspiration, transpiration, the normalized difference vegetation index, above-ground biomass, and ecosystem respirationare utilized as targets to assess the model's performance. Simultaneously, a neural network (NN) is trained to predict the model parameters, using input features(to the NN) such as plant functional types, climate types, bioclimatic variables, atmospheric nitrogen and phosphorus deposition, and soil properties. The model simulation is executed within our internal framework Sindbad.jl (to be open-sourced), designed to ensure compatibility with gradient-based optimization methods.This work serves as a stepping stone, demonstrating that incorporating neural networks into a broad collection of physics-based models holds significant promise and has the potential to leverage the abundance of current Earth observations, enabling the application of these methods on a larger scale.