The congress > Guest Speakers

Alain Oustaloup, IMS UMR 5218
Title: The FPM model, a single simple and predictive model for predictions in epidemiology, climatology, and economics

Abstract – Recognized as a “CNRS Highlight of 2021” and initially designed for the spread of the Covid-19 pandemic in 2020 (by combining internal complexity with overall simplicity), the FPM (Fractional Power Model), or non-integer (or fractional) power model, is a simple and predictive model that makes it possible to represent simply or to predict accurately the evolution of complex phenomena. Those addressed to date, and for which the model stands out through its predictions, include infections and vaccinations in epidemiology, CO₂ concentration in the atmosphere, air and water temperature and mean sea level in climatology, as well as France’s debt in economics. Like the linear regression that it generalizes, the FPM model has the advantage of dispensing with any hypothesis; its computation and predictions use exclusively real data, through which only reality impacts the model parameters and its predictions. Its representativeness (of complexity) is due to its ability to represent an unlimited number of internal dynamics with different speeds, such as those of an epidemic, from the slowest, originating in very sparsely populated rural areas, to the fastest, originating in very densely populated cities. The model indeed admits an integral form (a jewel of the model) that is established via non-integer integration and that continuously defines the dispersion of internal dynamics. Its predictiveness is due to its ability to take into account the entire past by weighting it appropriately. The model is indeed endowed with a predictive long-memory form (another jewel), established via non-integer differentiation, which expresses that any predicted value is a function of all past values, values that prove to be favorably weighted according to a forgetting factor (which is not without evoking a subtle form of memory). The model thus has the advantage of making the best possible use of the past, all the more so since only the past can be used to predict the future—indeed, a predictive specificity of a nature that makes this model a good predictor for decision-makers.

Biography of Alain Oustaloup – A graduate of ENSEIRB in 1973, Alain Oustaloup is currently Professor Emeritus at ENSEIRB-MATMECA – Bordeaux INP. After synthesizing complex non-integer differentiation or integration, then overcoming the stability–accuracy dilemma in control engineering and the mass–damping dilemma in mechanics, he invented CRONE control and CRONE suspension. More recently, he has done so again by proposing a new non-integer power predictor, which he applies in epidemiology, climatology, and economics. His work has been recognized by a CNRS Silver Medal in 1997 and a Grand Prize of the French Academy of Sciences in 2011.