Internal Research Fellow (PostDoc) in Theory of Deep Learning

This research fellowship will be undertaken in ESA’s Advanced Concepts Team (ACT), ESA’s internal research think tank for advanced space concepts and technologies. The ACT is a highly multidisciplinary group of postdoctoral fellows and early-career researchers who work in close partnership with leading universities to explore ideas that are still far from mainstream space engineering but could become disruptive in the future. The team operates to high academic standards, publishes in peer-reviewed journals and conferences, and has built 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 on emerging trends and acts as a pathfinder for novel technologies and working methods across all space domains.

The overarching goal of this research fellowship is to develop and study advanced theoretical frameworks for deep learning, understand their mathematical foundations, and connect them to space-related technologies and missions. The focus is on building rigorous models that explain and predict the behaviour of modern neural networks, covering representation, optimisation, generalisation, robustness and reliability, while remaining sufficiently tractable to inform engineering practice. A key objective is to transform theoretical advances into practical insight and tools that can support analysis, design and decision-making for AI-enabled space systems, thereby bridging the emerging scientific theory of deep learning with high-impact space applications.

In recent years, the ACT has carried out a broad range of projects at the interface between artificial intelligence and space engineering, introducing event transition tensors and Taylor models as tools to map neural systems onto mathematically well-understood objects. Pioneering the field, the ACT has developed several innovations, including deep learning for guidance, navigation and control, visual landing and event-based vision, scientific deep learning for physical systems, and spiking neural networks for event-based systems. Building on this experience, the research line on the theory of deep learning will investigate questions such as the structure and expressivity of emerging neural architectures relevant to space, such as implicit neural fields, continuous normalising flows, flow matching, neural ODEs, as well as graph neural networks.

Looking forward, the aim is to develop new mathematical and computational paradigms that can deepen our scientific understanding of deep learning and expand its safe use in space. This includes, but is not limited to, approaches based on statistical mechanics and thermodynamics of learning, dynamical systems and continuous-time views of neural networks, information-theoretic and optimal-transport perspectives on representation and generalisation, probabilistic numerics and Bayesian deep learning, and emerging frameworks for scientific deep learning that integrate physical constraints, symmetries and conservation laws. A central ambition is to connect these theories to concrete ACT projects and ESA use cases, such as autonomous guidance and navigation, data-driven modelling of spacecraft and environmental dynamics, mission planning and operations, and on-board learning in resource-constrained environments.

Our team and mission

You will take scientific ownership of a research line on the theory of deep learning within the ACT, with a strong emphasis on understanding and advancing the mathematical foundations of modern neural networks for space-relevant applications. Within the ACT’s collaborative environment, research topics are defined jointly, but you, as a Research Fellow, will be expected to drive the scientific agenda, identify promising directions, and lead the corresponding developments, while contextualising your work within the ACT scientific roadmap where appropriate.

Scientifically, you will:

• propose and conduct original research on the mathematical foundations of deep learning, developing novel theoretical frameworks, models and analytical tools to advance the understanding of modern neural networks;
• investigate fundamental questions related to the behaviour of deep neural networks, including expressivity, optimisation, generalisation, representation learning, continuous-time architectures (e.g. neural ODEs, flow matching and continuous normalising flows), robustness, interpretability and uncertainty quantification;
• collaborate with researchers across the ACT to identify emerging theoretical challenges motivated by astrodynamics, optimisation, control, scientific machine learning, mission design and autonomous systems, translating these into new research directions in deep learning theory;
• contribute to, and benefit from, ongoing and past ACT research activities, such as the development of certification methods for neural decision-making systems (e.g. using event transition tensors and Taylor models), while bringing new theoretical perspectives and extending these approaches where appropriate;
• monitor emerging neural architectures, theoretically analyse their properties, and identify those with the highest potential for early adoption in space engineering;
• translate theoretical advances into algorithmic innovations, design principles and prototype tools that can be integrated into the ACT's simulation, analysis and optimisation workflows, fostering the adoption of mathematically grounded machine learning methods in space applications.

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 deep learning theory and artificial intelligence with areas such as mission analysis, guidance and control, optimisation, space systems, unconventional computing and fundamental physics;
• participate, together with the team, in the assessment of innovative space-system concepts, and propose new deep-learning-based models and studies that can inform and enable such concepts, for example in autonomous operations, scientific data analysis or intelligent payloads;
• 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 theoretical and computational advances.

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

Behavioural competencies

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

Education

You should have recently completed (within the past five years), or be close to completion of a PhD in artificial intelligence, or a closely related field, with a strong track record in mathematical analysis of advanced neural systems.

Additional requirements

You should have:

• Ability for and interest in prospective interdisciplinary research;
• Aptitude to contextualise specialised areas of research and quickly assess 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 regarding 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 multi-cultural 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

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

Please note that applications can only be considered from nationals of one of the following States: Austria, Belgium, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Luxembourg, the Netherlands, Norway, Poland, Portugal, Romania, Slovenia, Spain, Sweden, Switzerland, and the United Kingdom. Nationals from Cyprus, Latvia, Lithuania and Slovakia, as Associate Member States, or Canada as a Cooperating State, can apply as well as those from Bulgaria, Croatia and Malta as European Cooperating States (ECS).

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.