Yvon Maday

Yvon Maday is a Professor in Applied Mathematics at the Sorbonne University (formerly University Pierre et Marie Curie) where he is currently the director of the Carnot Institute (aiming at developing partnership-based research between public laboratories and socio-economic players, primarily industries). Before this, he was the director of the Laboratoire Jacques-Louis Lions. He is also a senior Member of the Institut Universitaire de France and a Member of the European Academy of Sciences. He received the Blaise Pascal prize from the French Academy of Sciences in 1991, the Jacques-Louis Lions prize from the French Academy of Sciences in 2009, the Atos–Joseph Fourier Prize in Scientific Computing in 2018 and the 2019 ICIAM Pioneer Prize.


We repost here an extract from the interview to Prof. Yvon Maday, published in the Mathesia Outlook on Data Science: a report exploring how Data Science and Applied Mathematics will shape our future.


What do you reckon as the most interesting problem you have faced within the broad field of data science?
I have two answers in this matter. The first answer is in the pure research context where, I have worked on the problem of data assimilation guided by a given parameter dependent model for the phenomenon under investigation. By using this model (with imperfections that we name bias), represented through a model reduction, and the data, derived from measurements polluted with noise, we propose an approximate solution that corrects both the bias and the noise. This method named the PBDW method (for Parameterized-Background Data- Weak) has, by the way, been proven in a recent paper to be an ‘optimal recovery’ in the Hilbert space framework within a certain class of approaches.

The second answer is related to a recent collaboration with a company where we have used a large (not huge though) number of data owned by the company combined with data grabbed from open repositories. The purpose was to predict the number of tourists interested in visiting a project attraction and help in the decision whether it is worth opening it. By understanding the expertise of the company, we have proposed a model that has been able to structure the data in subsystems so as to hook different neural networks that have achieved a better prediction than the pure unique network in which all the data were entered that we tested first (and would certainly have been sufficient if we would have got a larger in time history of data).

What have been the biggest successes of data science so far?
The design of autonomous and connected vehicles is to my opinion one of the major successes of the collaboration between applied mathematics, software engineering and artificial intelligence.
It is still also one of the challenging problems that, for instance, will have to involve perception, decision in emergency situations that will also require collaborating with experts in behavioural and human sciences.

In what application field would you say data science will truly make a difference in the coming 4 – 5 years?
One field of importance is the application of the combined knowledge of models and data science (non data sciences) in high-dimensional systems, like in molecular dynamics for instance. There have recently been very interesting approaches in this field, proposed by various teams, to get a mapping from the geometric structure of a molecule to output like energy or forces and this may for instance provide a new approach for fast and automatic solutions to the parameterization of force fields. Another application of interest for me is the ability, based on an AI approach, to propose a domain decomposition reflecting a learned classification of the regimes of the solution so as to use of each subdomain the ad-hoc reduced basis to perform, by glueing local reconstructions, a good approximation of the solution.

What do you expect will be the research challenges, critical issues and risks data science will have to cope with in the near future?
I think that one critical issue is the collaboration between data scientists, applied mathematicians and experts in the application under investigation in order to model their expertise and nourish the proposed model with adequate data. One important aspect of this tri-party collaboration would be to define which data is adequate and the best way to collect it.