Process-Informed Neural Networks: A Hybrid Modelling Approach to Improve Predictive Performance and Inference of Neural Networks in Ecology and Beyond.

Despite deep learning being state of the art for data-driven model predictions, its application in ecology is currently subject to two important constraints: (i) deep-learning methods are powerful in data-rich regimes, but in ecology data are typically sparse; and (ii) deep-learning models are black-box methods and inferring the processes they represent are non-trivial to elicit. Process-based (= mechanistic) models are not constrained by data sparsity or unclear processes and are thus important for building up our ecological knowledge and transfer to applications. In this work, we combine process-based models and neural networks into process-informed neural networks (PINNs), which incorporate the process knowledge directly into the neural network structure. In a systematic evaluation of spatial and temporal prediction tasks for C-fluxes in temperate forests, we show the ability of five different types of PINNs (i) to outperform process-based models and neural networks, especially in data-sparse regimes with high-transfer task and (ii) to inform on mis- or undetected processes.