The Center for Applied Mathematics (CMA) is developing an original scientific approach by applying its fundamental scientific skills in modelling and the mathematics of control and decision-making to tackle the issue of decarbonisation of complex systems on a multi-scale basis, covering both time and space. This original stance, which combines fundamental mathematics and climate issues, is the culmination of a visionnary scientific strategy that was initiated some twenty years ago. Energy issues associated with climate change and globalisation provided the opportunity for a thematic renewal in the mathematics of decision making, a field in which the laboratory has a great deal of expertise, notably with the recent development of data mining. Research projects at the CMA are organised along three axes:
Prospective modelling
Meeting the challenges of carbon neutrality and sustainable development requires government decision-makers and businesses a capacity for coherent long-term anticipation and an awareness of the complexity and interdependencies between technological innovation, economic impact, lifestyles and environmental objectives. The central proposal of the CMA’s prospective modelling research axis is therefore to develop optimisation models that allow energy choices to be formalised and studied in their systemic and intertemporal dimension. This research activity involves modelling energy systems on regional, national, continental and global scales, as well as creating and running the Chair Modelling for Sustainable Development.
Mathematical optimisation
The design and operation of complex systems with a view to decarbonising them raises new theoretical and practical questions in mathematical optimisation: how can we deal with the non-convex, non-differentiable dynamics of these physical systems, in conjunction with uncertainties in predictive data or discrete decisions and logical operating conditions, on multiple and large temporal and spatial scales?
Where engineering problems of high complexity and large dimensions have historically been dealt with using simplified optimisation models and dedicated heuristic algorithms, the CMA employs a methodological approach, studying general classes of mathematical programs, designing versatile algorithms with guaranteed convergence, and applying them to detailed models, particularly on decision-making problems relating to energy production and consumption.
Data and machine learning
As a result of the digital transition that the energy sector has undergone in recent decades, data-based models are an ideal complement to traditional physics-based approaches. Indeed, the latter require a high level of detail, which can lead to an excessive computational load for certain analyses, such as operational forecasts requiring the generation of sets of forecasts via multiple simulations. As a result, less computationally intensive techniques, such as data-driven modelling, need to be considered. The low-carbon systems studied at the CMA are many and varied.
