Project Deep2PDE. Scientific report. Mixing data-driven and theory oriented approches for the modeling of complex systems: application to cocoa based agroforestry systems in Cameroon

Barczi Jean-François, Melatagia Yonta Paulin, Momo Stéphane Takoudjou, Nzegha Arnaud, Peynaud Emilie, Stinckwich Serge. 2020. Project Deep2PDE. Scientific report. Mixing data-driven and theory oriented approches for the modeling of complex systems: application to cocoa based agroforestry systems in Cameroon. s.n. : s.l., 42 p.

Résumé : Cocoa based agroforestry systems implemented in Cameroun are efficient and sustainable cropping systems. They provide many environmental, agronomic, but also socioeconomic services. They contribute to food security by diversifying the sources of farmers' incomes. A good understanding of such systems is required to optimize their management. Mathematical modeling is a great conceptual tool to acquire knowledge that can be used on top of experimental approaches. More specifically, mathematical models based on Partial Differential Equations (PDE) are able to describe the spatiotemporal dynamics of bio-physical phenomena. Research has been done to adapt this formalism to the modeling of plant growth. Still, there are difficulties identifying the right set of equations and calibrating the parameters and fully interpreting the equations in terms of plant growth. Deep learning and neural networks are now popular tools that can answer simple modeling questions by analyzing big sets of data. In particular, neural networks require a lot of data for their training. New technologies such as terrestrial LIDAR help us to acquire a huge number of precise measurements of cocoa trees in agroforestry systems. The idea behind the Deep2PDE project is to test the ability of neural networks to automatically identify the PDE that best simulates the dynamics of plant growth, and particularly of cocoa trees from measurements of their biomass spatio-temporal distribution. In the framework of the project, a non-exhaustive review of the use of neural networks to extract PDE from data has been conducted. Then, the most promising approaches were implemented and tested. Measurement campaigns have been done to collect data of cocoa trees in agroforestry systems in Cameron. First results and conclusions have been drawn about the use of this approach to help modelers to design models. Most importantly, thanks to this work, we conceptualized the scientific workflow called CEDI*tion that aims to find PDE models from data.

Mots-clés libres : Plant growth modeling, Agroforestry, Cocoa (Theobroma cacao), Partial differential equations, Physics informed neural networks

Auteurs et affiliations

• Barczi Jean-François, CIRAD-BIOS-UMR AMAP (FRA)
• Melatagia Yonta Paulin, Université de Yaoundé 1 (CMR)
• Momo Stéphane Takoudjou, Université de Yaoundé 1 (CMR)
• Nzegha Arnaud
• Peynaud Emilie, CIRAD-BIOS-UMR AMAP (FRA) ORCID: 0000-0002-2404-8098
• Stinckwich Serge, UNU (CHN)

Source : Cirad-Agritrop (https://agritrop.cirad.fr/613684/)

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