Mathematical and Agent-Based Modelling
Scientific objectives
The theme aims to advance the science of complex models by developing methods for analysis, validation and simplification. In particular, the aim is to gain a better understanding of model properties (stability, bifurcations, parameter sensitivity, uncertainties), and to propose reduction techniques that retain essential mechanisms while reducing computational costs.
A major focus is on the integration and coupling of models (hybridization), in order to link different scales of space and time. This makes it possible, for example, to articulate individual dynamics (agents) and global descriptions (equations), in fields such as epidemiology or transport.
The theme develops explanatory models to address general scientific questions and gain a better understanding of the mechanisms underlying observed phenomena. These models are used to test hypotheses, explore scenarios and analyze the role of certain factors (spatial heterogeneity, interactions, individual behavior).
They contribute, for example, to the study of collective dynamics or the analysis of complex ecological systems, by highlighting emergent properties that are difficult to observe directly.
The theme designs and maintains open-source tools to facilitate the creation, use and distribution of :
- simulation platforms (including GAMA),
- software libraries and dedicated languages,
- design, calibration and analysis tools.
Particular attention is paid to the interoperability, reproducibility and accessibility of these tools. The integration of recent advances in artificial intelligence also opens up prospects for assisting model design and coding, and extending their use to non-specialists.
Methodological developments are closely linked to concrete applications in the fields of environment, health, agriculture, and urban planning. Models are used both to understand the systems under study and to support stakeholders in decision-making, by enabling the exploration of scenarios and the evaluation of public policies.
Scientific challenges
Applications
The production of food resources and the sustainability of water resources are threatened by the development of human activities and the effects of climate change. These issues are addressed by our various partners' centers: Sahelian agro-sylvo-pastoral systems in a context of climate change in West Africa, bio-economy of fisheries in Senegal, North Africa and Vietnam (Brochier et al. 2021): identification of conditions to increase Maximum Sustainable Yield (Nguyen et al., submitted), study of the optimal placement of Marine Protected Areas (Ghouali 2022). A project on the development of sustainable and equitable offshore anchovy fishing and optimization of value chains near Phu Quoc Island off the Mekong Delta has just been submitted for funding by the Global Centre on Biodiversity for Climate (GCBC).
The Red River Delta, whose central area is the Bac Hung Hai region (Red River Delta) in northern Vietnam, a large agricultural region irrigated by a major canal network, is also a field of study for the unit's researchers as part of the LMI ACROSS8, associated since 2021 with UMMISCO. The study of water supply issues in this vast system is approached through hybrid modelling approaches between mathematical models (describing the system's hydrodynamic process) and agent-based models (describing the behaviours and interactions of the system's actors), enabling the multiple aspects linked to the sustainable and participatory management of irrigation systems to be addressed with all the necessary richness (Chien 2018).
Research focuses on the development of a mathematical approach based on the kinetic theory of active particles for modeling living systems and collective behavior. Kinetic and hyperbolic equations are used to describe phenomena such as multicellular systems in biology, the dynamics of crowds and swarms, and interactions in the social and economic sciences.
Within this framework, swarm theory is mobilized to represent emergent behaviors resulting from simple local interactions between agents, leading to global collective dynamics. This approach is particularly well-suited to the study of self-organizing systems and collective intelligence, such as the coordinated movements of animals (birds, fish, bees) or biological entities.
The aim of this work is to link microscopic and macroscopic descriptions within a unified kinetic framework, while developing appropriate scaling methods and numerical schemes.
Models are used to analyze and support the sustainable management of natural resources. This includes the study of fisheries (sustainable yield, marine protected areas), agricultural systems and irrigation networks.
Hybrid approaches are used to represent both physical processes (hydrology, climate) and the behavior of stakeholders (farmers, managers). This work contributes in particular to the evaluation of agro-ecological transition scenarios and the analysis of their environmental, economic and social impacts.
Activities
The theme's scientific leadership aims to strengthen exchanges between disciplines and geographical centers. It relies on :
- collaborative projects financed through internal calls,
- seminars, workshops and theme schools,
- technical activities such as coding camps around modeling platforms.
The theme also contributes to training (Masters, professional training) and the dissemination of knowledge to academic and institutional partners. A series of trans-disciplinary seminars will bring together different approaches to the same problem (mathematics, computer science, AI, social sciences).
