PhD in Safe AI-based Control

Neural networks can provide the flexibility needed to control increasingly complex dynamical systems, but their opaque and nonlinear behavior makes it difficult to guarantee safety and stability. How can we exploit the expressive power of machine learning without compromising the rigorous guarantees required in safety-critical control applications?

In this PhD project, you will develop methods for the analysis, verification, and design of neural-network-based controllers. Rather than treating safety and stability as properties to be assessed only after training, you will investigate safety- and verification-by-design approaches that incorporate certifiable properties directly into the controller architecture and learning process.

This project offers a unique opportunity to work at the intersection of machine learning and control theory. You will develop rigorous theory and scalable computational methods for certifying closed-loop safety and stability, with potential directions including control barrier and Lyapunov functions, quadratic constraints, semidefinite programming, and neural-network architectures with intrinsic stability or robustness properties. You will also investigate how physical insight, prior system knowledge, and stabilizing baseline controllers can be combined with learning to improve performance while retaining rigorous guarantees. The developed methods will be evaluated on benchmark problems and more realistic scenarios involving complex dynamical systems.

You will join the Control Systems Technology group in the Department of Mechanical Engineering. The group offers an open and collaborative environment that combines fundamental and applied research. Its expertise spans data-driven modelling of dynamical systems, control of complex and uncertain systems, motion control for high-tech systems, model predictive, networked, supervisory, neuromorphic, and learning-based control, cyber-physical systems, and optimization. This research is reinforced by close collaborations with industry. You will receive close scientific supervision while having the freedom to shape your research direction, present your work at international conferences, and develop as an independent researcher. Your work will contribute to the foundations of trustworthy artificial intelligence for control and support the reliable use of learning-based controllers in areas such as robotics, motion control, and energy systems.

PhD Position Equilibrium Behavior of Tramp Elements for Green Steel Production

Job description

The transition to low-carbon steel production is one of the key challenges in modern industry. At Tata Steel IJmuiden, this transition involves replacing the traditional blast furnace route with Direct Reduction, Electric Arc Furnaces (EAF), and, in a later stage, a Reducing Electric Furnace (REF). While these technologies enable significant CO₂ reduction, they introduce new challenges—most notably the accumulation of “tramp elements” from scrap and variable feedstocks, which can negatively affect steel quality and slag usability.

This PhD project aims to develop a fundamental thermodynamic understanding of how tramp and trace elements distribute between molten steel, slag, and vapor under next-generation steelmaking conditions. The research will focus on experimentally determining equilibrium partitioning behavior across relevant temperature, composition, and redox conditions, and translating these insights into predictive models for industrial application.

You will design and conduct high-temperature equilibration experiments using advanced gas-mixing furnaces at TU Delft and partner institutes. Samples will be analysed using state-of-the-art techniques such as laser ablation ICP-MS and electron microscopy to quantify trace element distributions at high spatial resolution. The resulting data will be integrated into thermodynamic models (e.g. FACTSage-based approaches) to support process optimisation and control in industrial steelmaking.

The project is carried out in close collaboration with Tata Steel R&D and academic partners, offering a unique opportunity to work at the interface of fundamental science and industrial application. You will contribute directly to the development of green steelmaking technologies while gaining expertise in high-temperature materials science, thermodynamics, and advanced analytical techniques.

Your profile

We are looking for a highly motivated candidate with a Master’s degree in Materials Science, Metallurgy, Chemical Engineering, Geoscience, or a related field. A strong interest in thermodynamics, high-temperature processes, and experimental work is essential. Experience with analytical techniques or modelling is an advantage.

• Design and perform high-temperature equilibrium experiments to study tramp element partitioning between steel, slag, and vapor phases
• Analyse experimental samples using advanced techniques (e.g. LA-ICP-MS, SEM/EDS) to quantify trace element distributions
• Develop and interpret thermodynamic datasets describing element behavior under EAF and REF conditions
• Integrate experimental results into thermochemical models (e.g. FACTSage) to support process simulation and optimisation
• Collaborate with researchers at TU Delft and Tata Steel IJmuiden, and communicate findings through reports and scientific publications

Job requirements

• MSc degree in Experimental Petrology, Materials Science, Metallurgy, Chemical Engineering, Geoscience, or a closely related field
• Strong interest in thermodynamics, high-temperature processes, and experimental research
• Affinity with or experience in laboratory work and materials characterization techniques (e.g. SEM, ICP-MS)
• Basic knowledge of thermodynamic modelling or willingness to learn tools such as FACTSage
• Analytical mindset with strong problem-solving skills and attention to detail
• Ability to work both independently and collaboratively in an interdisciplinary team
• Good communication skills in English (written and spoken)
• Motivation to engage with both academic research at TU Delft and industrial application at Tata Steel IJmuiden

TU Delft (Delft University of Technology)
Working at TU Delft means contributing to solutions that really make a difference.

For over 180 years, we have been training engineers who make an impact worldwide in companies, government bodies, or as entrepreneurs. Our alumni turn knowledge into concrete solutions for the challenges of today and tomorrow. These challenges are changing rapidly. That is why we focus on themes such as energy, climate, digitalisation, artificial intelligence (AI), and smart mobility every day. Our education and research are directly aligned with what society needs now and in the future.

At TU Delft, our people make the difference. With their knowledge and curiosity, our staff provide a high-quality education and conduct pioneering research that extends beyond the campus. You will have the opportunity to take the initiative, work with others, and grow as a professional. Working at TU Delft means join an international community of professionals and students. Together, we create knowledge, innovations, and solutions that help move the world forward.

Faculty Aerospace Engineering
The Faculty of Aerospace Engineering at Delft University of Technology is a leading international community where innovation in aerospace meets global challenges. Our support and scientific staff, including PhD candidates, postdocs, and students, largely work together on three main themes: the energy transition, sustainable aerospace, and safety and security, with the aim of tackling climate change and contributing to the independence and security of Europe.

When you join us, you become part of a diverse, collaborative, and forward-thinking environment where your ideas and perspectives are valued. Our work extends beyond the lab—into field labs, innovation hubs, and partnerships with other faculties, research institutes, governments, and industry, both locally and globally.

We are committed to fostering an inclusive and welcoming workplace, assisted by an active Diversity & Inclusion team. This includes tangible support such as funding for extra personnel for family and caregiving responsibilities, mentoring programmes, and initiatives that promote cultural exchange and integration.

You don’t just join our faculty — you join a community where you can thrive, grow, and help shape the future of aerospace.

Click here to go to the website of the Faculty of Aerospace Engineering.

Student assistent Universiteit Leiden (ca 12 uur per week)

Vacature: Student assistent Universiteit Leiden (ca 12 uur per week)

Vacature: Student assistent Universiteit Leiden (ca 12 uur per week)
De Universiteit Leiden heeft een aantal profileringsthema’s benoemd, waaronder het thema ‘duurzaamheid en biodiversiteit’. Een groep onderzoekers, elk vanuit een andere discipline en faculteit, gaat Universiteit Leiden beter zichtbaar maken op dit strategische thema, en het trans- en interdisciplinair onderzoek en onderwijs voor duurzaamheid en biodiversiteit verder aanjagen.

Het team van onderzoekers wordt ondersteund door een programma coördinator, en zoekt per september 2026 een student assistent. De student assistent gaat ondersteunen bij administratieve taken, het organiseren van bijeenkomsten en de communicatie.

Wanneer, hoeveel uur, waar?
Van 1 september 2026 tot en met 31 augustus 2027, voor 12 uur in de week (0.315fte). We hanteren een proefperiode van twee maanden. Je zal op kantoor in Leiden werken (Van Steenis Gebouw), online en soms op andere locaties in Leiden.

Het Team
Je gaat deel uitmaken van een team van collega’s die werken aan gelijksoortige opdrachten. Binnen de Leiden-Delft-Erasmus samenwerking - het Centre for Sustainability en het programma Klimaat en Biodiversiteit - werken community- en programmamanagers aan trans- en interdisciplinair onderwijs en onderzoek en het opbouwen van netwerken, elk vanuit een eigen opdracht. Ook de coördinator van het Leiden Biodiversity Network (LBN) werkt vanuit dit team. Het LBN brengt kennisinstellingen en maatschappelijke partners samen rondom biodiversiteit.

We delen een kamer, waar ook de student assistent een plek krijgt. Ons team werkt op maandag (en donderdag) op kantoor in Leiden, de overige dagen hebben we een flexibele agenda en werken we ook online. De student assistent werkt het liefst op maandag - en anders op donderdag - tenminste een dagdeel in Leiden. De overige uren kunnen vanuit huis worden gewerkt. Er is tweewekelijks een online meeting met de onderzoekers die werken aan het strategische thema.

Deze baan past bij je, als je:

• Zelfstandig en accuraat kan werken.
• De Nederlandse en Engelse (C2) taal uitstekend beheerst in woord en geschrift.
• Handig en ervaren bent met online tools voor mailing, webbeheer en vormgeefprogramma’s, zoals Spotler, Drupal en Canva
• Ervaring hebt met het organiseren van (online) evenementen en activiteiten.
• Goede communicatievaardigheden hebt.
• Heldere en bondige teksten kan schrijven.
• Je je in je opleiding met biodiversiteit of duurzaamheid hebt beziggehouden, of op andere manier kan aantonen affiniteit en kennis te hebben van het onderwerp.
• Je bent (binnen grenzen en in overleg) flexibel inzetbaar en vindt het geen probleem de ene week wat meer en de andere week wat minder uren te maken als het werk daarom vraagt.

Dit bieden we je
Je werkt samen met topwetenschappers, die bevlogen zijn om het onderwijs en onderzoek nog meer interdisciplinair op te zetten, om nog beter antwoord te kunnen geven op de grote en urgente uitdagingen van deze tijd. Je krijgt de kans ervaring op te doen met vormgeven, communicatie en eventmanagement. Administratie is een belangrijk deel van de opdracht.

De aanstelling vindt plaats bij Universiteit Leiden. Het salaris bedraagt tussen de €3.320- en €3.288,- bruto per maand bij een fulltime aanstelling, afhankelijk van je studiejaar en ervaring (schaal van student assistent).

Solliciteren of meer weten?
Stuur je cv met een korte motivatie naar LDE_CfS@cml.leidenuniv.nl (contactpersoon: Ester Segers) voor donderdag 20 augustus (13:00 uur). Als je vragen hebt kun je mailen naar dit e-mailadres. De gesprekken vinden plaats op donderdag 27 augustus, tussen 13 en 16 uur, in Leiden.

PhD position in modeling the mechanical regulation of plant development and regeneration (1.0 FTE)

The Faculty of Science, the Mathematical Institute and the Institute of Biology are looking for a PhD Student in Theoretical or Mathematical Biology

What you will do
The opening is for a research position within the field of mathematical or theoretical biology, computational physics, applied mathematics or computational science. This PhD project is part of the Gravitation programme GreenTE (Green Tissue Engineering), a multidisciplinary consortium of 7 Dutch universities. Together, GreenTE will unravel how plants sense and respond to mechanical stimuli. These fundamental insights will be the basis to develop engineering interventions to improve plant regeneration, seed longevity and defenses against disease. Your task will be to further develop two-dimensional and three-dimensional models of plant development, incorporating mechanical feedback loops to regulate cellular decision making and polarization. The goal will be to unravel how plant shape and size is regulated by feedback loops between the tissue and organ levels and cellular and molecular levels. The project will further develop a two-dimensional open source package for modeling plant tissues, called Virtual Leaf, which coupled a Hamiltonian description of cell wall strains and stresses and turgor pressures with sets of ordinary differential equations describing the biochemical networks regulating cellular decision making. Models will be initiated with simulated data and 2D and 3D imaging data of plant tissues (the thale cress Arabidopsis and the aquatic fern Ceratopteris). At a later stage, the models can be extended to three dimensions using software developed concurrently by a postdoc in our team.

The successful applicant will be an integral member of the GreenTE community, which offers an open, diverse and inspiring environment to engage in multidisciplinary mechanobiology research at the intersection of biology, chemistry and physics, and is expected to participate in GreenTE events, training and collaborations.

Key responsibilities

• Develop and interpret novel two-dimensional multiscale mathematical models of mechanical regulation of plant development and regeneration in close collaboration with members of the GreenTE consortium, in particular the group of experimental plant biologist Prof.dr. Dolf Weijers at Wageningen University.
• Further develop the plant modeling package VirtualLeaf to reflect mechanical manipulation as performed in the experimental lab (https://www.mathbioleiden.nl/software.html#virtualleaf).
• Incorporate detailed insights into the model of the mechanical properties of cell walls based on experiments and small-scale simulations developed elsewhere in the GreenTE consortium.
• Correct and improve your mathematical models in close collaboration with experimental biologists, particularly PhD students at Wageningen University who will perform mechanical interventions (e.g., stretching, squeezing or poking) of embryo development and root regeneration of the model plant Arabidopsis thaliana.
• At a later stage: extend the models to three dimensions based on Virtual Leaf3D currently under development by a postdoctoral researcher in our team
• Publication of the results in the scientific literature and writing a PhD thesis.
• Co-teaching of relevant courses and student supervision.

Where you will work

Research at our faculty
The Faculty of Science is a world-class faculty where staff and students work together in a dynamic international environment. It is a faculty where personal and academic development are top priorities. Our people are committed to expand fundamental knowledge by curiosity and to look beyond the borders of their own discipline; their aim is to benefit science, and to make a contribution to addressing the major societal challenges of the future.

The research carried out at the Faculty of Science is very diverse, ranging from mathematics, information science, astronomy, physics, chemistry and bio-pharmaceutical sciences to biology and environmental sciences. The research activities are organised in eight institutes. These institutes offer eight bachelor’s and twelve master’s programmes. The faculty has grown strongly in recent years and now has more than 2.300 staff and almost 5,000 students. We are located at the heart of Leiden’s Bio Science Park, one of Europe’s biggest science parks, where university and business life come together.

For more information, see www.universiteitleiden.nl/en/science and http://workingat.leiden.edu/

The Mathematical Institute (MI) is one of the eight institutes within the Faculty of Science and has a strong international orientation. The institute's mission is to push the boundaries of scientific knowledge by developing and applying high-quality mathematics while offering a wide range of mathematical programs in a friendly and intellectually stimulating environment. We believe that mathematics is a fundamental part of human knowledge, and we take pride in our role as guardians of this rich scientific discipline. We are dedicated to expanding the frontiers of mathematical knowledge and applying our expertise to solve challenges in other sciences, society, and industry. Additionally, we actively promote mathematical literacy through various outreach activities.

The Mathematical Institute focuses on four key research themes: Algebra, Geometry, and Number Theory; Analysis and Dynamical Systems; Probability; and Statistics and Data Science. There is extensive collaboration between these themes. For more information about the Mathematical Institute, see https://www.universiteitleiden.nl/en/science/mathematics.

Multiscale Mathematical Biology - The work will be embedded in the interdisciplinary Multiscale Mathematical Biology (MMB) team at the Mathematical Institute and the Institute of Biology Leiden, both at the Faculty of Science at Leiden University, and is also part of the qBioLeiden (https://www.universiteitleiden.nl/quantitative-biology) initiative that unites research in quantitative biology at Leiden University. The MMB team carries out mathematical biology research in close interaction with its own experimental work and that of collaborators. The team focuses on the mechanobiology of animals and plants. More information about the group can be found on http://www.mathbioleiden.nl

What you bring

• Master’s degree in applied numerical mathematics, computational/theoretical physics, theoretical biology, computer science, or a related discipline;
• Written and oral proficiency in English, strong scientific writing skills;
• Ability to work independently in collaboration with a multidisciplinary environment;
• Fluent interdisciplinary communication skills with scientists in cell biology and mathematics;
• Keen interest in cell and developmental biology of plants;
• Experience in (numerical) mathematical modeling (e.g., vertex-based or Cellular Potts modeling, particle-based simulations, PDEs, FBA);
• Suitable programming skills in C++ or a related language

What we offer
Our goal is to work together to create a transparent and inclusive work environment in which everyone feelswelcome and appreciated. Our organisation is always evolving and we need your ideas for improvement and innovation to take us further. We want to devote attention to your personal development.

You can count on an enjoyable job within the socially relevant world of education and research. The University's challenging and international work environment is located just steps away from Leiden’s lively city centre. We also want to work with you to devote attention to your health and vitality, for example with the fun activities we organise through Healthy University.

We also offer:

• An employment contract for the duration of one year with a view to permanent employment. This contractfalls under the CLA of Dutch Universities;
• A salary between € 3204 - € 4051 gross per month, based on a full-time appointment (38 hours) (PhDstudent);
• A holiday allowance (8%), an end-of-year bonus (8,3%), and an attractive pension scheme at ABP;
• Full reimbursement of public transport commuting costs for home-to-work travel;
• Flexible working hours: as a standard, you are entitled to a minimum of 29 leave days on the basis of afull-time working week of 38 hours; you can also save for extra leave, for example by working 40 hours aweek, and in this way accrue an extra 96 leave hours, or exchange 96 leave hours for a 36-hour week.
• Lots of options when it comes to secondary employment conditions; within our terms of employmen tindividual choices model, you can exchange leave days and/or salary for benefits such as anadvantageous sports subscription and bicycle scheme;
• A home-working allowance (day and internet allowance) and attention for good workplaces. The University will also provide you with a laptop.

For more information about employment conditions, see Application process and working conditions - Working at Leiden University - Leiden University

All our PhD candidates are embedded in the Leiden University Graduate School of Science.

What we value
Promoting an inclusive community is central to Leiden University’s values and vision. We strive to be an open community in which all students and staff members feel valued and respected, and are able to fully develop themselves. We consider an inclusive academic environment, where students and staff can share their experiences and viewpoints, to be essential for the development of talent.

Want to apply or find out more?
If you want to apply straight away, click the application button. Please ensure that you join to your application the following documents:

• A letter of motivation
• An updated CV
• The transcripts of your MSc studies
• A copy of (a draft of ) your Master’s thesis
• Contact details of 1 or 2 former supervisors who may be contacted during the selection process
• Examples of previously written code

Applications received before September 15th, 2026 will be given full consideration.

Starting date: fall or winter 2026, flexible.
If you would like more information about what the job entails, please contact Prof.dr. Roeland Merks, at merksrmh@math.leidenuniv.nl.