Internal Research Fellow (PostDoc) in Applied Math and Advanced Numerics

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.

Our team and mission

Field(s) of activity/research for the traineeship

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.

Scientifically, you will:

• 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, optimisation, control, uncertainty quantification, inverse problems and related areas of space research;
• develop reusable and robust computational methods that can be integrated into ACT simulation, analysis, and optimisation workflows, with attention to efficiency, scalability and mathematical soundness;
• translate abstract mathematical ideas into practical tools and modelling strategies for space-related technologies, systems analysis and mission-enabling applications;
• interface with scientific and engineering data, where appropriate, to test, calibrate and benchmark proposed methods, and to guide the development of mathematically grounded solutions.

As an ACT researcher, you will:

• publish results in peer-reviewed journals and conferences, and share tools, software and methodological developments through seminars, open-source repositories and outreach activities inside and outside ESA;
• initiate and contribute to interdisciplinary projects with other ACT researchers, combining applied mathematics and advanced numerics with areas such as mission analysis, guidance and control, optimisation, AI, space systems or unconventional computing;
• participate together with the team in the assessment of innovative space-system concepts, and propose new mathematical models and numerical studies that can inform and enable such concepts;
• benefit from, and contribute to, the technology and engineering expertise available at ESTEC, including access to numerical infrastructure, mission studies and technical specialists relevant for validating and applying the developed methods.

Behavioural competencies

• Result Orientation
• Operational Efficiency
• Fostering Cooperation
• Relationship Management
• Continuous Improvement
• Forward Thinking

Technical competencies

• Knowledge relevant to the field of research
• Research/publication record
• Ability to conduct research autonomously
• Breadth of exposure coming from past and/or current research/activities
• Ability to gather and share relevant information
• General interest in space and space research

Education

You should have recently completed (within the past five years), or be close to completion of a PhD in applied mathematics, computational science, physics, engineering or a closely related field, with a strong track record in numerical modelling, mathematical analysis and the development of computational methods for complex systems.

Additional requirements

• Ability for and interest in prospective interdisciplinary research;
• Aptitude for contextualising specialised areas of research and quickly assessing their potential with respect to other domains and applications;
• Academic networking to add functioning links to universities and research institutes;
• Ability to work in a team, while being able to work individually on your own personal research plans and directions;
• Natural curiosity and a passion for new subjects and research areas;
• Proficiency in computer programming and data analysis;
• Good interpersonal and communication skills and the ability to work in a multicultural environment, both independently and as part of a team;
• A good knowledge of English or French is required. Knowledge of another Member State language would be an asset.

Important Information and Disclaimer

Applicants must be eligible to access information, technology, and hardware which is subject to European or US export control and sanctions regulations.

Successful candidates will need to undergo basic screening before appointment, which will be conducted by an external background screening service, in compliance with the European Space Agency's security procedures.

Nationality and Languages

Please note that applications can only be considered from nationals of ESA Member States, Associate Member States, Canada as a Cooperating State, and certain European Cooperating States, in accordance with ESA eligibility rules.

According to the ESA Convention, staff shall be recruited on the basis of their qualifications, taking into account an adequate distribution of posts among nationals of the Member States.