Section: Overall Objectives
In recent years, a new generation of numerical algorithms have begun to spread through the scientific community. Surprisingly enough, up to a few exceptions, many of these modern ideas do not really come from physics, but from biology and ethology. In a growing number of scientific disciplines, the researchers are now interpreting real world processes and engineering type systems less like purely deterministic and crude clockwork mechanisms, but much more like random and sophisticated biology inspired processes. This new generation of engineering models is based on stochastic ideas and natural principles like : Chance, randomness, interactions, reinforcement strategies, exploration rules, biology-inspired adaptation and selection transitions, learning, reproduction, birth and death, ancestral lines and historical processes, genealogical tree evolutions, as well as self-organization principles, and many others.
These biology-inspired stochastic algorithms are often presented as natural heuristic simulation schemes without any mathematical foundations, nor a single performance analysis ensuring their convergence, nor even a single theoretical discussion that clarifies the applicability of these models. An important aspect of our project is to create a concrete bridge between pure and applied probability, statistics, biology, stochastic engineering and computer sciences. This fundamental bridging effort is probably one of the most important key to turn real nature's processes into engineering devices and stochastic algorithms, by learning what can be abstracted, copied or adapted. In the reverse angle, we can mention that these abstracted models adapting nature mechanisms and biological capabilities also provides a better understanding of the real processes.
By essence, the team-project is not a single application-driven research project . The reasons are three folds: Firstly, the same stochastic algorithm is very often used in a variety of application areas. On the other hand every application domain area offers a series of different perspectives that can be used to improve the design and the performances of the algorithms. Last but not least, concrete industrial applications, as well as most of concrete problems arising in biology, physics and chemistry, require a specific attention. In general, we do not use a single class of stochastic algorithm but a broader set of stochastic search algorithms that incorporates facets of nature inspired strategies.
Our research project is centered on two central problems in advanced stochastic engineering: Bayesian inference and rare event simulation and more particularly unsupervised learning, multi-target tracking, spike sorting, data assimilation and forecasting, as well as infection spreads inference. These important and natural research directions have emerged as logical parts of the team project combined with interdisciplinary approaches well-represented at Bordeaux university campus.
The fundamental and the theoretical aspects of our research project are essentially concerned with the stochastic analysis of the following three classes of biology inspired stochastic algorithms: branching and interacting particle systems, reinforced random walks and self-interacting processes, random tree based models. One of our prospective research project is to apply the Bayesian learning methodology and the recent particle filter technology to the design of a new generation of interactive evolutionary computation and stochastic art composition models.