I Am :
Share this page :
Research at the DISC

“Applied Mathematics” (AM) scientific group

Last Updated On

The “Applied Mathematics” (AM) scientific group covers a wide range of topics: stochastic processes (especially Markov processes), numerical optimization (especially multidisciplinary optimization) and parallel computing, stabilization, control and numerical solution of partial differential equations, and financial engineering.

Nos axes de recherche

Un des champs d’étude privilégiés, permettant de regrouper presque tous ces thèmes, est celui de l’étude théorique et numérique des problèmes liés aux interactions fluide-structure.

Ces actions de recherche se font en collaboration avec les grands acteurs toulousains : Institut de Mathématiques de Toulouse (Université Paul Sabatier-INSA), ONERA ou encore Institut Clément Ader (ICA), mais aussi avec d’autres partenaires nationaux et internationaux.

Le groupe de recherche de Mathématiques Appliquées (MA) est constitué de sept enseignants-chercheurs et un ingénieur-chercheur.

Les contributions sont principalement réalisées dans les thèmes de recherche suivants :

*Le découpage présenté ci-dessous n’est pas strict : des interactions existent.

Dans cet axe de recherche, on s’intéresse à divers aspects du contrôle et de la stabilisation ou stabilité de solutions à des équations aux dérivées partielles. Pour être plus précis :

  • Contrôle des équations aux dérivées partielles
  • Interaction Fluide-Structure
  • Systèmes Hamiltoniens à Ports d’Interactions (pHS)

L’idée sous-jacente aux systèmes Hamiltoniens à ports d’interactions est de décrire la dynamique d’un système à l’aide de l’énergie physique du système (appelé le Hamiltonien).

En particulier, cela permet de traiter de manière générale les non-linéarités (Hamiltonien non quadratique). L’analyse du problème de Cauchy associé est toujours un sujet actif de recherche dans le cas de systèmes de dimension infinie (typiquement des équations aux dérivées partielles non-linéaires).

Les ports d’interactions consistent classiquement en un contrôle et une observation (entre autres) colocalisés permettant de coupler différents pHs. Le système résultant est alors encore un pHs. Il existe des structures algébriques subordonnées aux pHs : les structures de Dirac.

La simulation numérique des pHs appellent des méthodes numériques particulières permettant de préserver le Hamiltonien (ou plus précisément l’existence d’une structure de Dirac associée au système discrétisé).

Notons également que la stabilisation en boucle fermée est facilement obtenue dans les pHs, et qu’ils permettent également, au moins en dimension finie, de prendre en compte des contraintes sous forme d’équations algébriques couplées au système dynamique.

  • Systèmes Différentiels Fractionnaires et Diffusifs (SDF)
  • Systèmes linéaires bien posés (Well-Posed Linear Systems : WPLS)

Dans cet axe de recherche, on s’intéresse à l’optimisation numérique et à l’optimisation multidisciplinaire dans le cadre de la conception avant projet. Pour être plus précis :

  • Développement et analyse d’algorithmes d’optimisations (déterministes et stochastiques)
  • Résolution de systèmes linéaires de grande taille et pré-conditionnement
  • Propagation d’incertitudes (UQ)
  • Analyse de sensibilité
  • Modèles de substitution
  • Calcul haute performance (HPC)

Dans cet axe de recherche, on s’intéresse à l’application des probabilités et de la statistique à des problèmes concrets rencontrés par les industriels. Pour être plus précis :

  • Analyse de performance des réseaux de communication
  • Analyse de sensibilité
  • Arbres aléatoires

Nos partenaires

Michel FOURNIE
Michel FOURNIE

Responsable Groupe MA

Annuaire

Découvrez les profils des 130 enseignants-chercheurs de l'Institut qui font progresser la recherche en aéronautique et spatial.

Cette ressource vous permet d'explorer les domaines et projets de recherches des scientifiques de l'école !

Accès à l'annuaire

Offres d'emploi

Consultez les offres d'emploi pour les personnels scientifiques du département de recherche !

Offres de thèses

Consultez les offres de thèses et de post-doctorat du département de recherche !

Offres de stage

Consultez les offres de stage du département de recherche !

Related Content

View Other Pages

Videos

Sylvestre Maurice, astrophysicist and ISAE-SUPAERO alumnus

Awarded a prize by the Académie des Sciences in 2020, Sylvestre Maurice #astrophysicist at the Institut de Recherche en Astrophysique et Planétologie (IRAP) in Toulouse witnessed the landing of the #Perseverance rover on Mars on February 18, 2021. A historic moment for this enthusiast, who is also the scientific manager of the onboard SuperCam instrument. A 1990 graduate of ISAE-SUPAERO, Sylvestre Maurice tells us about his career.

Alumni

Researcher

Space

Pages

“Photonics Antenna Microwave PlasmaA” (PAMPA) scientific group

The “Photonics Antenna Microwave PlasmaA” (PAMPA) scientific group is interested in electromagnetism in the fields of microwaves and photonics, as well as wave-plasma interactions.

DEOS

Doctoral student

PhD

Events

ISAE-SUPAERO will be at the Paris Air Show at Le Bourget from June 16 to 22, 2025

ISAE-SUPAERO will be present at the 55ᵉ Salon International de l'Aéronautique et de l'Espace at Le Bourget from June 16 to 22, 2025!

Aeronautics

Event

Space

Events

"Les Entretiens de Toulouse - Training through debate”: April 9 & 10, 2025 on the ISAE-SUPAERO campus

"Les Entretiens de Toulouse" has become a must-attend event for the aerospace industry. A forum for the exchange and transmission of skills, this training through debate provides an opening onto subjects with high industrial stakes. The 2025 edition of the Entretiens de Toulouse will take place on April 9 & 10, 2025, in person, at ISAE-SUPAERO!

Aeronautics

Event

Innovation

Pages

Aerodynamics, Energetics, and Propulsion Department (DAEP)

At ISAE SUPAERO, the Aerodynamics, Energetics, and Propulsion Department has a staff of 62, 30 research projects including 5 on a European scale, an exceptional fleet of test facilities for teaching and research purposes, and three research groups contributing to a growth strategy focused on 4 themes of current scientific and social-economic challenge, supported by 2 structuring projects: the SAA wind tunnel and the IC3 large-scale simulation code.

DAEP

PhD

Researcher

Pages

Complex Systems Engineering Department (DISC)

Within ISAE-SUPAERO, the Complex Systems Engineering Department (DISC) develops skills in mathematics and computer science for aeronautical and space engineering. In both teaching and research, it focuses on the models, methods, and tools needed to control the behavior and performance of complex systems. This complexity may be induced by the multi-physics or multi-scale nature of the systems studied, their dynamic behavior, or their distributed and communicating structure.

DISC

PhD

Researcher

Pages

Job offers

Aeronautics

Decarbonization

Internship

Pages

Our semesters & short programs

Aeronautics

Aerospace summer program

Semester research project

Pages

Languages, Arts, Cultures, and Societies Department (LACS)

At the Languages, Arts, Cultures, and Societies Department (LACS), we teach languages, interculturality, geopolitics, general culture, economics, sports, etc. Multidimensional skills that bring out knowledge, interpersonal skills, know-how and interpersonal skills.

LACS

PhD

Researcher

Videos

Training courses: space studies

Find out more about our courses and #information in the field of space! The space dimension is strongly developed within our various training courses, whether in specific streams or dedicated programs. French and international students alike are showing a keen interest in our educational programs in Earth observation and the sciences of the Universe, as well as in the design and operation of space systems. Space research and industry employ many ISAE-SUPAERO engineers. Explore the world of space!

Program

Space

Pages

Design and Operation of Aerospace Vehicles Department (DCAS)

At ISAE-SUPAERO, the Design and Operation of Aerospace Vehicles Department (DCAS) develops methods, simulation tools and experimental platforms for the design and operation of aerospace vehicles.

DCAS

PhD

Researcher

News

Mission Insight: the contribution of researchers from ISAE-SUPAERO

The InSight lander deployed by NASA recorded two earthquakes that occurred on Mars in 2021, providing scientists with exceptional data, the first direct observations ever made of a planet's core.

DEOS

Space

Testimonials

Testimony of Juan-Carlos DOLADO-PEREZ, alumni of the 2008 Master's degree in Aerospace Engineering

Alumni

Space

Testimonial

Pages

Our certificates of specialized studies

Our certificates of specialized studies are designed for professionals. They enable you to develop skills and expertise in the fields of digital, aeronautics, space, project management, systems engineering and artificial intelligence.

Aeronautics

Certificates of advanced studies

Short internship

Pages

Lasbordes Air Operations Center (COAL)

The Design and Operation of Aeronautical and Space Vehicles Department (DCAS) is part of the Lasbordes Air Operations Center (COAL), located on an airfield a few kilometers from the ISAE-SUPAERO campus. As part of its aeronautical training and research activities, COAL operates a fleet of 9 light aircraft.

DCAS

Doctoral student

PhD

Videos

FRENCH SUPERCAM INSTRUMENT RECORDING THE SOUND OF INGENUITY'S 4th FLIGHT

Located 80 meters from the rover at the moment of take-off, the small helicopter rose to 5 meters above the ground before covering a distance of 133 meters before returning to land where it had taken off from. SuperCam's scientific microphone, developed by ISAE-SUPAERO, recorded the sound emitted by the rotation of the Martian drone's blades during its flight. This sound has a characteristic frequency of 84 Hz, equivalent to the low “E” of a piano or the bass voice of a human being. “This is a big surprise for the whole scientific team,” says Naomi Murdoch, a researcher at ISAE-SUPAERO who is studying the data from the microphone. "Tests carried out in a Martian atmosphere simulator to design this instrument, and our theories of sound propagation, indicated that the microphone would have great difficulty picking up the sounds of the helicopter. Indeed, Mars' thin atmosphere strongly attenuates sound transmission. We needed a bit of luck to record the helicopter from such a distance. We're very pleased to have succeeded in obtaining this recording, which is proving to be a goldmine for our understanding of the Martian atmosphere". Developed jointly by ISAE-SUPAERO and a consortium of CNRS laboratories and its partners, coordinated by CNES, SuperCam's microphone is derived from a consumer model adapted to withstand the Martian environment. It pursues 3 substantial scientific and technical objectives of the Mars 2020 mission: Study the sound associated with laser impacts on Martian rocks, to gain a better understanding of their mechanical properties. Improving our understanding of atmospheric phenomena (wind turbulence, dust eddies, wind interactions with the rover, and now with the helicopter). Understanding the sound signature of the rover's various movements (robotic arm and mast operations, driving on normal or uneven ground, pump monitoring, etc.). The microphone was first switched on a few hours after Perseverance landed. It recorded the first Martian sounds generated by turbulence in the atmosphere. It is used daily in conjunction with laser rock ablation for chemical analysis of Mars. ABOUT THE MARS 2020 MISSION: NASA is relying on Caltech's Jet Propulsion Laboratory for the development of the Mars 2020 mission. SuperCam was developed jointly by LANL (Los Alamos National Laboratory, USA) and a consortium of laboratories attached to the CNRS, French universities and research establishments. Several Spanish universities, led by the University of Valladolid, are also contributing to the instrument. CNES is responsible to NASA for the French contribution to SuperCam. The instrument is operated alternately from LANL and the French Operations Center for Science and Exploration (FOCSE) at CNES in Toulouse.

DEOS

Researcher

Space

News

The project for an unmanned, zero-emission aircraft to cross the South Atlantic

Innovation

Researcher

Sustainability

News

Let's make together a durable commitment to new horizons

Aeronautics

Horizons

Sustainability

Videos

A surprise from elsewhere... from the ISS...?

Hello earth? Thomas Pesquet speaking! Thomas Pesquet, French astronaut and famous ISAE-SUPAERO alumnus (class of 2001), is currently in the ISS as part of his new Alpha mission. He sent our students a personalized message from the European laboratory Columbus...

Alumni

Diversity program

Space

Pages

“Navigation, Radar and Remonte Sensing” (NAVIR² eS) scientific group

The “Navigation, Radar and Remonte Sensing” (NAVIR² eS) scientific group is interested in the theoretical study of information sources and hybridization approaches for autonomous vehicle navigation applications.

DEOS

Doctoral student

PhD

Pages

Validation of prior experience

The validation of prior experience is an individual right enshrined in the French Labor Code and Education Code. It enables candidates to obtain all - or part - of a professional certification (Diploma, Professional Title, Certificate of Professional Qualification), based on their professional, salaried or non-salaried and/or voluntary experience. This scheme can be used if the candidate is seeking personal recognition, or more generally to support a professional project that he or she wishes to put into practice.

Aeronautics

Certificates of advanced studies

Company

Pages

Research

DAEP

DCAS

DEOS

Pages

“Communication and Information Theory” (ComiT) scientific group

The “Communication and Information Theory” (ComiT) scientific group is involved in the disciplines of digital communications, radar, and channel access techniques. Its fields of application include space systems, civil and military aviation, terrestrial cellular networks and the Internet of Things (IoT).

DEOS

Doctoral program

Doctoral student

Events

Les Assises du New Space 2025: discussions and debates on NewSpace!

The 2025 edition of the Assises du New Space will be held this year on July 8-9, 2025 at the Centre des congrès de la Villette - Cité des sciences et de l'industrie in Paris. Aimed at all players in the French space ecosystem, this event is a unique opportunity to exchange ideas and debate around NewSpace, and to discover the latest technological innovations and project financing opportunities. Registration is now open!

Conference

Event

Round table

News

ISAE-SUPAERO publishes an aviation and climate report

Sustainability

Teacher researcher

Pages

“Space Systems for Planetology and Applications” (SSPA) scientific group

The “Space Systems for Planetology and Applications” (SSPA) scientific group focuses on one main area of research: the development of missions and associated technologies for geophysical exploration of the solar system.

DEOS

Doctoral student

PhD

Videos

Discover the portrait of Anthéa COMELLINI doctoral student at ISAE-SUPAERO

Anthéa completed her thesis in the Complex Systems Engineering Department (DISC). Her thesis is entitled “Vision-based autonomous rendezvous with non-cooperative targets”. Anthéa is attached to the AA - Aéronautique Astronautique doctoral school. Her thesis, carried out in collaboration with Thales Alenia Space, is part of the CIFRE* program ISAE-SUPAERO hosts its doctoral students in six teams at ISAE-SUPAERO, ONERA and the Clément Ader Institute, covering a broad spectrum of scientific disciplines related to aeronautics and space: aerodynamics and propulsion, structures and materials, onboard systems, networks and telecommunications, systems control and operation, human factors, electronics, signals. ISAE-SUPAERO offers a rich and diversified doctoral training program, leading to the doctorate, the highest level diploma awarded by the institute, and recognized internationally. *Since 1981, the CIFRE scheme - Conventions Industrielles de Formation par la REcherche (Industrial Conventions for Training through Research) - has enabled companies to benefit from financial assistance to recruit a young doctoral student whose research, supervised by a public research laboratory, will lead to the completion of a thesis in three years. CIFREs are fully funded by the French Ministry of Higher Education and Research, which has entrusted ANRT (Association Nationale de la Recherche et de la Technologie) with their implementation.

PhD

Pages

Directory

Teacher researcher

Pages

“Connected Systems” (SysCo) scientific group

The scientific dynamic of the “Connected Systems” (SysCo) scientific group focuses primarily on network-related issues in aerospace applications, i.e. space communications, embedded networks and certain types of connected systems.

DISC

Doctoral student

PhD

Pages

Scientific and research integrity

ISAE-SUPAERO is one of the signatories of the National Charter of Ethics for Research Professions, adopted in January 2015 by the Conference of University Presidents (CPU) and all national research organizations, and incorporated into the Institute's internal regulations.

DAEP

DCAS

DEOS

Videos

Discover the portrait of Paolo PANICUCCI doctoral student at ISAE-SUPAERO

Paolo has completed his thesis in the Complex Systems Engineering Department (DISC). His thesis is entitled: Navigation based on autonomous vision and shape reconstruction of an unknown asteroid during the approach phase. It is attached to the AA - Aéronautique Astronautique doctoral school. ISAE-SUPAERO hosts its doctoral students in six teams at ISAE-SUPAERO, ONERA and the Clément Ader Institute, covering a broad spectrum of scientific disciplines related to aeronautics and space: aerodynamics and propulsion, structures and materials, embedded systems, networks and telecommunications, systems control and operation, human factors, electronics and signals. ISAE-SUPAERO offers a rich and diversified doctoral training program, leading to the doctorate, the highest level diploma awarded by the institute, and recognized internationally. Link to his thesis: http://www.theses.fr/s253653

PhD

Pages

“Integrated Image Sensors” (CIMI) scientific group

The “Integrated Image Sensors” (CIMI) scientific group, develops and characterizes active-pixel image sensors (CMOS Image Sensors (CIS)) on silicon for visible and infrared radiation.

DEOS

Doctoral student

PhD

Pages

“Design and Analysis of Critical Systems” (CASC) scientific group

The “Design and Analysis of Critical Systems” (CASC) scientific group focuses on methods, processes and tools to support System Engineering and Systems Engineering.

DISC

Doctoral student

PhD

Pages

“Theory, Modeling and Systems Engineering” (ThéMIS) scientific group

The “Theory, Modeling and Systems Engineering” (ThéMIS) scientific group is dedicated to the study and development of advanced methods for the design, modeling and validation of complex systems.

DISC

Doctoral student

PhD