Parametric Identification: estimation of model parameters and evaluation of estimation uncertainty
Evaluate model robustness and determine confidence intervals for the parameters are crucial for applications. A new perspective is currently studied to improve parametric estimation and uncertainty characterization of FSPMs, compared to the classical methods of Generalized Least Square types. An equivalent description of the dynamic system in the framework of hidden (latent variable) models was formulated (cf. Cournède et al., 2011). Statistical estimation in this framework can be tackled with tools borrowed from the theory of hidden Markov models, such as maximum likelihood estimation. Simulation-based methods are in progress in order to implement proper stochastic versions of the EM algorithm and stochastic gradient methods for state and parameter estimation. In this direction, the class of sequential Monte-Carlo, particle ﬁlter and MCMC algorithms, can be used for maximum likelihood estimation and seems particularly adapted to our case. The same type of methods can be used in Bayesian inference. It is also explored for situations in which priors are easy to determine (study of genetic populations, data assimilation, etc.).
Application to real plants: with the multiple objectives of improving, validating, comparing models and testing our estimation methods, the collaborations with ITB (for sugar beet), INRA-Grignon (for rapeseed), Supagro Montpellier (for Sunﬂower and Grapevine), Cirad-INRA Ecofog in Guyana (for Cecropia), CIRAD AMAP (for coffea), China Agricultural University and Chinese Academy of Forestry (for pine) – among others – are precious partnerships that make possible to get good datasets on different types of plants with different levels of details.
Given the multiplicity of plant growth models that are currently developed, it seems interesting to compare them, conceptually and mathematically, in order to assess their differences and select the ’best’ models regarding speciﬁc objectives. It can provide adequate tools for developing a benchmarking for Functional Structural Plant Models.
Optimization of experimental protocol for phenotyping
Once good estimation of the uncertainty in model parameters is obtained, it is possible to consider optimization of the experimental protocols. This is particularly important in phenotyping for seed companies, that need to evaluate the performances of large numbers of new varieties each year. The optimization concerns the amount of data to collect in a given experimental situation, and the number of experimental situations (with respect to climatic scenarios).
Data acquisition from aerial images and data assimilation
Using real data is the key to decrease model uncertainty. For this purpose, aerial, satellite or drone images provide a very interesting source of information. The objective is to assimilate this data, in order to:
- characterize plant population (species, positions, functional characteristics, etc.),
- correct and improve model prediction.