Internal Research Fellow; PostDoc in Applied Math and Advanced Numerics

Job Requisition

Closing Date: 16 July 2026 23:59 CET/CEST

Directorate:
Technology, Engineering and Quality

This research fellowship will be in ESA’s Advanced Concepts Team (ACT), ESA’s internal research think tank for advanced space concepts and technologies. The ACT is a multidisciplinary group of postdoctoral fellows and early‑career researchers who work in close partnership with leading universities to explore ideas that are still a long way off from becoming part of mainstream space engineering, but might prove disruptive in the future.

The team operates to high academic standards, publishes in peer‑reviewed journals and conferences, and has built up a broad European and international network through its collaboration schemes and open‑science activities. Through its research, the ACT provides ESA with early scientific insight into emerging trends and acts as a pathfinder for novel technologies and working methods across all space domains.

The overarching goal of the research line is to develop and study advanced mathematical approaches, apply them to space‑related technologies, and implement their solutions as cutting‑edge, efficient numerical methods. The focus is on building rigorous frameworks that can capture the complexity of challenging aerospace and space systems while remaining computationally tractable. A key objective is to transform theoretical advances into practical tools that can support analysis, design and decision‑making in a space engineering context, thereby building a bridge between pure mathematics and high‑impact space applications.

In recent years, the ACT has carried out a broad range of projects in this area, exploring topics such as Hamilton‑Jacobi Bellman equations, stochastic optimisation frameworks, game‑theoretical analysis of space logistics, high‑order automated differentiation, neural and Hamiltonian ODEs, data‑driven dynamical systems, perturbative theories in celestial mechanics, symbolic regression, inverse methodologies via differentiable simulations, efficient high‑dimensional numerical quadrature and more. These efforts have led to the development of widely used open‑source software tools, including heyoka, pyaudi, pagmo/pygmo, pykep, dSGP4 and torchquad, which provide the broader community with access to the relevant numerical methods.

Looking forward, the research line explicitly aims to welcome new mathematical theories and computational paradigms, with the goal of connecting them to ACT projects and space applications. This includes, but is not limited to, stochastic differential equations, stochastic partial differential equations, variational and geometric methods, probabilistic numeric, optimal transport, and other emerging frameworks that may offer new ways to model, analyse, and optimise complex space systems.

You are strongly encouraged to familiarise yourself with the ACT’s research portfolio, in particular its applied mathematics and advanced numerics, as well as the team’s other main research lines (for example AI for guidance, navigation and control, unconventional computing and fundamental physics), via the ACT website (https://(Use the "Apply for this Job" box below).).

You will take scientific ownership of a research line in applied mathematics and advanced numerics, with a strong emphasis on developing or applying advanced mathematical approaches to build computational frameworks capable of addressing challenging space‑related problems. Within the ACT’s collaborative environment, research topics are defined jointly, but you will be expected to drive the scientific agenda, identify promising directions and lead the corresponding developments, while contextualising your work within the ACT scientific agenda where appropriate.

• Propose and conduct original research on advanced mathematical and numerical topics relevant to space applications, with a focus on developing new theories, methods and computational approaches rather than merely extending existing work.
• Design, analyse, and validate innovative numerical algorithms and mathematical frameworks for problems arising in materials, fundamental physics, dynamics,…