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Système informatique d'aide à la modélisation mathématique basé sur un langage de programmation dédié pour les systèmes dynamiques discrets stochastiques.Application aux modèles de croissance de plantes.

Abstract : In agriculture, in order to predict crop yield or to reduce inputs, mathematical models of plant growth open new perspectives by simulating crop growth in interaction with the environment. In this thesis we will particularly focus on ”mechanistic” models based on the description of ecophysiological and archictectural processes in plants.Since the first attempts, in the seventies, the scientific community has created a large number of models with va- rious objectives : for instance, CERES, STICS, APSIM, LNAS as crop models and LIGNUM, ADEL, GreenLab, MAppleT as functional-structural models.These models have to be designed and evaluated with a rigourous process in several steps, according to what is usually described as ”good modelling practices”. The methods involved in the different steps are : sensitivity and uncertainty analysis, parameter estimation, model selection, data assimilation, optimal control ... According to the configuration of the study case, various algorithms can be used at each of these steps. The state-of-the-art software systems generally focus on one aspect of the global workflow, but very few focus on the workflow itself and propose the whole chain of mathematical methodologies adapted to the type of models and configurations faced in plant growth modelling : stochastic and nonlinear dynamical models involving a lot of processes and parameters, heterogeneous and irregular system observations.This thesis considers the formalization of stochastic dynamical models, of statistical methods and algorithms dedicated to their study and of the interface between models and algorithms to generate the analysis workflow. We deduce the conception of a software platform which allows modelers (or more exactly modelling teams, since the activity is quite complex) to create and validate crop/plant models by using a single language and dedicated statistical tools. Our system facilitates model design, sensitivity and uncertainty analysis, parameter estimation and evaluation from experimental data and optimization.Our research is at the heart of ”quantitative agronomy” which combines agronomy, modeling, statistics and computer science. We describe and formalize the type of models faced in agronomy and plant sciences and how we simulate them. We detail the good modelling practices workflow and which algorithms are available at all steps. Thanks to this formalization and tools, model studies can be conducted in an easier and more efficient way. It is illustrated on several test cases, particularly for the LNAS and STICS models. Based on this conception and results, we also discuss the possibility to deduce an ontology and a domain-specific language in order to improve the communication between experts. Finally, we conclude about the perspectives in terms of community platforms, first generally for modellers, and second more specifically in quantitative agronomy.
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Benoit Bayol. Système informatique d'aide à la modélisation mathématique basé sur un langage de programmation dédié pour les systèmes dynamiques discrets stochastiques.Application aux modèles de croissance de plantes.. Autre. Université Paris Saclay (COmUE), 2016. Français. ⟨NNT : 2016SACLC032⟩. ⟨tel-01367744⟩

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