Post-Doctoral Research Visit F/M Inverse problem in elasticity with wave separation

Inria, the French national research institute for the digital sciences; France; Hybride; EUR 40 000 - 50 000; Plein temps

Résumé du poste

A research institution in France is offering a two-year postdoctoral position focused on computational inverse problems. The successful candidate will develop new inversion techniques for elastic media while collaborating with the Makutu team. Ideal candidates will have a solid background in applied mathematics and prior experience in computational nonlinear inversion. The role offers flexible hours and opportunities for professional development.

Prestations

Partial reimbursement of public transport costs

Possibility of teleworking

Professional equipment provided

Access to vocational training

Social security coverage

Qualifications

• Strong background in inverse problems and applied mathematics.
• Experience with partial differential equations related to wave propagation.
• Desirable experience in computational nonlinear inversion.

Responsabilités

• Develop new inversion techniques for elastic media.
• Lead the development of software tools for wave separation.
• Write reports and prepare scientific publications.

Connaissances

Inverse problems

Applied mathematics

Partial differential equations

Computational nonlinear inversion

Scientific computing

Formation

PhD in a relevant field

Outils

Hawen open-source platform

Discontinuous Galerkin methods

Description du poste

Inria, the French national research institute for the digital sciences

Organisation/Company Inria, the French national research institute for the digital sciences
Research Field Computer science Mathematics Researcher Profile Recognised Researcher (R2) Country France Application Deadline 31 Dec 2025 - 00:00 (UTC) Type of Contract Temporary Job Status Full-time Hours Per Week 38.5 Offer Starting Date 1 Jan 2026 Is the job funded through the EU Research Framework Programme? Horizon Europe - ERC Reference Number 2025-09382 Is the Job related to staff position within a Research Infrastructure? No

Offer Description

We propose a two-years postdoc opportunity in computational inverse problems in the context of the ERC‑StG European project Incorwave which aims to develop advanced numerical and mathematical strategies for passive imaging. This postdoctoral position focuses on developing new inversion techniques for elastic media, where body waves play a critical role, and can be decomposed into Primary (P) waves (compressional) and Secondary (S) waves (shear). Traditional inversion methods treat these waves as coupled (working with the full displacement), but separating them offers significant potential to improve the accuracy of the inversion. The successful candidate will spearhead the development of cutting‑edge methods and sophisticated software tools designed to efficiently compute P‑ and S‑wave components. To achieve this, we will rely on Discontinuous Galerkin methods which are capable of handling complex discontinuities in the solutions, ensuring high‑fidelity wave separation. Once the waves are decomposed, the successful candidate will lead the inversion process for the separated P‑ and S‑wave components, and develop the appropriate strategy for optimal reconstructions. This will directly contribute to the project's overarching goal of improving passive seismic imaging. The research aims to provide more detailed and accurate subsurface characterisations, which are crucial for a wide range of applications, from geophysical exploration to monitoring subsurface processes.

The program will be divided into two main phases which corresponds to the modelling of the decoupled elastic waves, and the quantitative inversion. All software development and numerical implementation will be performed in the open‑source code Hawen (https://ffaucher.gitlab.io/hawen-website/) developed in the team Makutu, with help from the developer's team.

Phase 1: modelling

The first phase of the project focuses on the efficient numerical solution of the decoupled P‑ and S‑wave systems, which form the foundation for subsequent inversion tasks. The successful candidate will begin by deriving the corresponding pseudo‑differential equations that govern the propagation of these separated waves. Special attention will be given to the mathematical structure of the decoupled systems to ensure physical consistency and numerical stability. To solve these equations, the candidate will investigate Discontinuous Galerkin (DG) discretisation techniques, which are well‑suited for handling the discontinuities of the separated body waves.

Phase 2: inversion

In Phase 2, the nonlinear inverse problem will be addressed. The first step involves deriving the adjoint‑state formulation corresponding to the governing equations obtained in the previous phase. This derivation is essential for computing the gradient of the misfit functional efficiently, enabling large‑scale optimisation. Following this, the candidate will explore computational strategies to improve the performance and stability of the inversion process. A key aspect of this investigation will focus on the optimal selection and use of data (whether P‑wave, S‑wave, or combined datasets) in relation to the physical parameters being reconstructed (e.g., Lamé parameters, density, anisotropic properties). The goal is to design an inversion framework that maximises sensitivity to the targeted model parameters. In addition, one could also study the separation of partial data, for instance using learning techniques.

The applicant will review the bibliography and develop an appropriate framework for elastic wave separation and hierarchical inversion. They will be responsible for the computational implementation and testing. The role also involves writing reports or scientific papers and presenting results at international conferences. As a member of the Inria Makutu team, the applicant will collaborate with the group to support and enhance its activities.

The applicant must have a solid background in inverse problems and applied mathematics, in particular for partial differential equations related to wave propagation. Numerical implementation will be carried out within the open‑source platform Hawen, so prior experience in computational nonlinear inversion is highly desirable. Knowledge in scientific computing and familiarity with programming is also beneficial. In addition to the research and development work, the applicant is expected to contribute to the dissemination of results through the preparation of scientific publications and participation in international conferences.

Languages FRENCH Level Basic

Languages ENGLISH Level Good

Additional Information

• Partial reimbursement of public transport costs
• Possibility of teleworking and flexible organisation of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

Selection process

Thank you to send:

• CV
• Cover letter
• Support letters (mandatory)
• List of publications