ROOTS:Research on sOil Organic carbon dynamics,numerical and data-driven meThods for Spatial pattern

The ROOTS project focuses on studying the dynamics of soil organic carbon (SOC) using innovative numerical methods and data-driven techniques to understand SOC spatial patterns and promote sustainable land use. SOC is essential for soil health, enhancing water retention, nutrient availability, and erosion resistance. The project consists in the study of reaction-diffusion-chemotaxis models, including the MOMOS model, to explain soil aggregation and microbial organization. The project aims to address the following topics:

• Numerical methods for reaction-diffusion-chemotaxis models: develop numerical methods  that preserve, with no limitations on the discretization step length, the properties of the continuous solution, such as positivity and asymptotic behavior. This study will also include a theoretical analysis of the stability and convergence of the proposed methods.
• Data-driven techniques: the analysis of hidden structures in real data using a data-driven model not only can help to understand physical phenomena but is also essential for forecasting future developments more efficiently. These methods are directly applied to discrete temporal datasets, in principle without the knowledge of a given mathematical model behind. The goal of this research line is the use of data-driven techniques applied to experimental spatiotemporal data for making predictions. This step is important for soil microbial ecology and agricultural sustainability.
• Physics-Informed Neural Networks (PINNs) : in the context of soil microbial ecology, we aim at using PINNs to infer the spatial distribution of microbial communities and deduce the values of certain parameters from real data. By taking into account the physical processes governing microbial dynamics into the neural network, PINNs can provide accurate and interpretable solutions to complex inverse problems.