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Thomas Romary

Thomas Romary

Professor

Center · STIM

Discipline(s)
Applied Mathematics

Keywords

Team

STIM

Biography

Thomas Romary is a researcher whose work focuses on geostatistical modeling, deep learning applied to the geosciences, and uncertainty analysis in environmental and industrial systems. His research addresses a variety of issues, ranging from the stochastic simulation of geological reservoirs using generative adversarial networks (GANs) to the optimization of electronic waste (WEEE) characterization using advanced statistical methods. He also explores biogeochemical dynamics in aquatic environments, particularly through Bayesian approaches to estimate the properties of heterotrophic bacteria and the biodegradability of dissolved organic carbon. His expertise extends to the application of data assimilation methods, such as the ensemble Kalman filter or the particle filter, to improve water quality modeling and the prediction of spatiotemporal fields. Thomas Romary also contributes to industrial challenges, such as in-situ uranium recovery or the detection of vibrations during drilling, by integrating artificial intelligence techniques and physical models to enhance the robustness of the proposed solutions.

Publication(s)

Teaching

Differential, Integral, and Stochastic Calculus I (Math1)

Course Director

This first module of UE11 will begin with an introduction to the topology of metric spaces: open sets, closed sets, density, completeness, compactness, and the space of continuous maps between metric spaces. We will then cover the essential elements of measure theory (without doing all the proofs in lecture), which allows us to define the Lebesgue integral; we will clarify how it differs from the Riemann integral covered in preparatory classes. This integral will allow us to define the main functional spaces used in the mathematical study of equations in physics—the Lp spaces—and in particular the L2 space. We will then study Hilbert spaces (of which L2 is an archetypal example), which are generalizations of Euclidean spaces to infinite dimensions, and we will examine their main properties, in particular the existence of so-called Hilbert bases. The final part of the course will be devoted to differential calculus for mappings from R^n to R^m: the concept of a partial derivative, the differential of a mapping, the finite increase theorem in R^d, the implicit function theorem, and the local inversion theorem. Advanced tutorial sessions will allow motivated students to go beyond the concepts required for the exam: more in-depth analysis of measure and integration theory, functional analysis, Banach spaces, the Hahn-Banach theorem, operators in infinite-dimensional spaces, Sobolev spaces… This theoretical course aims to provide the foundations that will enable students to tackle the major challenges of applied mathematics, in particular the study and numerical solution of differential equations, partial differential equations, and optimization.

Differential, Integral, and Stochastic Calculus II (Math2)

Course Director

EC2 consists of two modules: Differential Equations and Probability. The differential equations course aims to introduce students to the study of dynamical systems: existence, uniqueness, and regularity of solutions to a differential equation (Peano–Arzela, Cauchy-Lipschitz, regularity with respect to initial conditions in finite time, chaotic systems), as well as an introduction to the study of the asymptotic behavior of solutions (periodic cycles, asymptotic stability of equilibrium points, etc.) An introduction to the simulation and numerical analysis of differential equations is also provided (discretization schemes, consistency/convergence analysis, differences between explicit and implicit schemes for stiff systems, the role of symplectic schemes for Hamiltonian systems, etc.) The probability course aims to consolidate and supplement the knowledge of probability theory acquired in CPGE, but above all to develop probabilistic reasoning. In CPGE, probability was studied in the context of random phenomena with at most a countable number of possible outcomes. Probabilities defined on the real line, as well as real random variables and vectors, are first introduced within the general formalism of measure theory—covered in EC1—which allows for the inclusion of the discrete case. The concepts of independence and conditioning of random variables, sequences of random variables, and finally stochastic simulation methods are addressed in turn to cover all the prerequisites necessary for the various engineering specializations offered at the school, particularly data science.

Water and Energy Flows (PI MOLONARI)

Lecturer

Elective Course Period (October and January)

Course Director

Geostatistics

Course Director

General Introduction and Introduction to the R Software (www.r-project.org) Random Function Models Inference and Prediction (Kriging and Simulations) Spatio-Temporal Modeling

Geostatistics and Applied Probability (GEOSTAT) track

Course Director

Regardless of the field of study and the problem at hand, an elective project based on real-world data always involves three aspects: an analysis phase, that is, a critical examination of the available data and an assessment of its suitability for the problem at hand. This simply involves rigorously defining what is being discussed, expressing—if necessary—in scientific terms what is expected from the study, and ensuring that the project has a reasonable chance of success; a modeling phase, because raw data can never be directly manipulated. It is therefore necessary to convert physical measurements into mathematical entities to which the theoretical frameworks covered in the various courses offered at the School can be applied; a synthesis phase, since developing a model is not an end in itself. After mathematical processing, we must therefore find ways to interpret what we have uncovered, even if this means revisiting one or more of the previous steps… In a sense, this first experience in applied geostatistics serves as an introduction to a certain code of ethics regarding the handling of numerical data. In this exercise, the educational effort directed toward external partners who propose research topics is obviously essential. By the end of their third year, students taking this elective have gained an initial overview of issues related to the manipulation of spatial data, and they have grappled in the field with the challenge of reconciling mathematical rigor with the demands of reality. They can now put this introduction to good use, regardless of the career path they choose upon graduating from the School. It is highly likely, in fact, that their professional career will now be in the service of a specific industrial sector that will likely have little connection to what they encountered during their elective work; but because of its fundamental and broad-based nature, the training they have received in this track will certainly prove applicable, even if the term “Geostatistics” is no longer explicitly mentioned! Some representative elective topics covered in recent years: numerical models of oil reservoirs; mining estimates and simulations; simulation of flu epidemics; processing of biological or physical data in oceanography and limnology; assimilation of spatiotemporal data in meteorology and climatology; analysis and modeling of pollution data (air, soil, waterways); automatic classification of gemstones; study of the correlation between urban morphology and energy consumption; automatic semantic analysis. Special features of the track: We wish to avoid “monochromatic” cohorts where everyone would focus on petroleum, or mining, or the environment... Furthermore, students are asked to “embrace their specialization” as soon as they choose their track at the end of their first year; it is particularly important that they communicate their preferences regarding the focus of their specialization project as soon as possible, even if the geostatistics courses themselves have not yet begun: this will enable us to offer them “tailored” guidance in the direction they have chosen. For students interested in topics related to quantitative finance, the track—even though it does not include courses directly related to the subject—allows them to complete their final thesis in this field. A few supplementary courses that can be taken in this case are listed below.

PhD supervision

  • 2026 4D Stochastic Weather Generator and High-Resolution Downscaling REYNAL François
  • 2025 Generative modeling of heavy-tailed distributions and extreme rainfall events FASSINA Tiziano
  • 2025 Effective methods for spatiotemporal model estimation LORET Alexandre
  • 2022 Stochastic two-dimensional structural geomodeling using deep generative adversarial networks GARAYT Charlie
  • 2021 Deep Generative Models for Conditional Spatial Simulation BHAVSAR Ferdinand
  • 2020 High-frequency data assimilation in the ProSe-PA water quality model - Factors of river metabolism under low-flow conditions HASANYAR Masihullah
  • 2020 Urban Mines and Sampling of Waste Electrical and Electronic Equipment (WEEE) BARTHET Alexis
  • 2020 Spatio-temporal prediction by stochastic partial differential equations CLAROTTO Lucia
  • 2017 Quantification of uncertainties in uranium deposit exploitation by In Situ Recovery LANGANAY Jean
  • 2016 Simulation of the Seine River metabolism through continuous data assimilation WANG Shuaitao