PhD Diagnostics for interconnected complex dynamical systems

Introduction
Are you passionate about mathematical systems and control theory? Are you interested in working with next generation high-tech systems? The main challenge lies in the reliable operation of the entire system, where many interconnected modules affect each other. In this project, you will be designing algorithms to guarantee the reliable operation of semiconductor machines, together with a highly innovative industrial partner in the Brainport region. If all these sounds fascinating, then this PhD position is made for you!

Job Description
We invite highly motivated students with a strong background in mathematical control theory, and a keen interest in machine learning to apply for the PhD position within the Dynamics and Control section at the Department of Mechanical Engineering, Eindhoven University of Technology. The mission of the Dynamics and Control Section is to perform research and train next-generation students on the topic of understanding and predicting the dynamics of complex engineering systems in order to develop advanced control, estimation, planning, learning and diagnostics strategies which are at the core of the intelligent autonomous systems of the future: Designing and realizing smart autonomous systems for industry and society.

Complex dynamical systems, such as semiconductor equipment, consists of many interconnected modules, which are functionally, digitally and physically interconnected. The throughput of the equipment relies on continuous runtime while meeting stringent requirements on accuracy and performance. Therefore, monitoring the health of these systems is crucial, which is now largely performed by human experts. The aim of this PhD project is to design innovative monitoring algorithms for complex dynamical systems to automate fault isolation with diagnostics performance guarantees.

Current health monitoring technology is typically designed for either (i) individual system components/modules (which would require removing the component from the system, which is not possible in practice), or (ii) for the system as a whole. The first approach fails to account for the interaction between modules and its effect on the whole system. The second approach makes it challenging to isolate which module may be failing and how to zoom in on the part of the system that is the root cause of the failure. This PhD position will address this challenge by developing hierachical diagnostic tools for complex dynamical systems.

Topics that you will delve into include:

• Interconnected dynamical systems
• (Distributed) Observer design
• Data-driven approaches
• Machine learning methods
• Fault detection and isolation

This PhD position is part of the project on ‘Holistic Design Automation for Semiconductor Manufacturing Equipment’, in which 6 PhD students will be employed at the Eindhoven University of Technology in the department of Mechanical Engineering, as well as the departments of Electrical Engineering and Mathematics and Computer Science. You will have the chance to collaborate with a semiconductor company, ASML to apply the developed results in an industrial context, thereby building both a strong academic and industrial profile.

You will have access to the graduate courses at the Dutch Institute of Systems and Control (DISC) and will have the opportunity to collaborate with industry in the Brainport region and academic researchers worldwide. By joining us, you will be part of a vibrant community of more than 60 researchers including faculty members, postdocs and PhDs working on diverse topics in the field of dynamical systems and control and its applications.

This PhD position is jointly supervised by Nathan van de Wouw, Tom Oomen and Michelle Chong.

Job Requirements

• A master’s degree (or an equivalent university degree) in systems and control, mechanical engineering, electrical engineering or applied mathematics.
• Strong background in mathematical systems and control theory.
• Experience and/or a keen interest in the field of hybrid dynamical systems, observer design, learning techniques, and optimization.
• Knowledge of at least one programming language: Matlab, Python, is expected.
• Eager to work within a team and independently.
• Ability to collaborate with industry and academic researchers.
• Fluent in spoken and written English.

Conditions of Employment
A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 - max. € 3,881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

About us
Eindhoven University of Technology is a leading international university within the Brainport region where scientific curiosity meets a hands-on mindset. We work in an open and collaborative way with high-tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact — today and in the future. TU/e is home to over 13,000 students and more than 7,000 staff, forming a diverse and vibrant academic community.

The Department of Mechanical Engineering department conducts world-class research aligned with the technological interests of the high-tech industry in the Netherlands, with a focus on the Brainport region. Our goal is to produce engineers who are both scientifically educated and application-driven by providing a balanced education and research program that combines fundamental and application aspects. We equip our graduates with practical and theoretical expertise, preparing them optimally for future challenges.

Information
Do you recognize yourself in this profile and would you like to know more? Please contact

• Dr. Michelle S. Chong, m.s.t.chong@tue.nl, https://www.michellestchong.com/
• Prof.dr.ir. Nathan van de Wouw, N.v.d.Wouw@tue.nl, http://vandewouw.dc.tue.nl/
• Prof.dr.ir. Tom Oomen, t.a.e.oomen@tue.nl

at the Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands.

Visit our website for more information about the application process or the conditions of employment. You can also contact HRadviceME@tue.nl or +31 40 2475902.

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video.

Are you inspired and would like to know more about working at TU/e? Please visit our career page.

Application
We invite you to submit a complete application by using the 'apply now'-button on this page. The application should include the following documents as a single PDF file::

• Curriculum vitae, including a list of your publications and the contact information of three references. Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.
• An explanation of your interest in the proposed research topic.
• Copies of diplomas and academic transcripts with grades from prior university studies.
• Brief description of your MSc thesis and/or relevant research projects.

Ensure that you submit all the requested application documents. We give priority to complete applications.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post.
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check, please consult the National Knowledge Security Guidelines.
• Please do not contact us for unsolicited services.

PhD Diagnostics for interconnected complex dynamical systems

We invite highly motivated students with a strong background in mathematical control theory, and a keen interest in machine learning to apply for the PhD position within the Dynamics and Control section at the Department of Mechanical Engineering, Eindhoven University of Technology. The mission of the Dynamics and Control Section is to perform research and train next-generation students on the topic of understanding and predicting the dynamics of complex engineering systems in order to develop advanced control, estimation, planning, learning and diagnostics strategies which are at the core of the intelligent autonomous systems of the future: Designing and realizing smart autonomous systems for industry and society.

Complex dynamical systems, such as semiconductor equipment, consists of many interconnected modules, which are functionally, digitally and physically interconnected. The throughput of the equipment relies on continuous runtime while meeting stringent requirements on accuracy and performance. Therefore, monitoring the health of these systems is crucial, which is now largely performed by human experts. The aim of this PhD project is to design innovative monitoring algorithms for complex dynamical systems to automate fault isolation with diagnostics performance guarantees.

Current health monitoring technology is typically designed for either (i) individual system components/modules (which would require removing the component from the system, which is not possible in practice), or (ii) for the system as a whole. The first approach fails to account for the interaction between modules and its effect on the whole system. The second approach makes it challenging to isolate which module may be failing and how to zoom in on the part of the system that is the root cause of the failure. This PhD position will address this challenge by developing hierachical diagnostic tools for complex dynamical systems.

Topics that you will delve into include:

• Interconnected dynamical systems
• (Distributed) Observer design
• Data-driven approaches
• Machine learning methods
• Fault detection and isolation

This PhD position is part of the project on ‘Holistic Design Automation for Semiconductor Manufacturing Equipment’, in which 6 PhD students will be employed at the Eindhoven University of Technology in the department of Mechanical Engineering, as well as the departments of Electrical Engineering and Mathematics and Computer Science. You will have the chance to collaborate with a semiconductor company, ASML to apply the developed results in an industrial context, thereby building both a strong academic and industrial profile.

You will have access to the graduate courses at the Dutch Institute of Systems and Control (DISC) and will have the opportunity to collaborate with industry in the Brainport region and academic researchers worldwide. By joining us, you will be part of a vibrant community of more than 60 researchers including faculty members, postdocs and PhDs working on diverse topics in the field of dynamical systems and control and its applications.

This PhD position is jointly supervised by Nathan van de Wouw, Tom Oomen and Michelle Chong.

PhD position on computational illumination optics

Introduction
Are you eager to use your mathematical skills to model and design optical systems for sustainable high-tech devices for billions of people? Do you like to develop and analyze numerical methods for partial differential equations?

Job Description
The Computational Illumination Optics group is one of the few mathematics groups worldwide working on mathematical models of optical systems. They develop and analyze numerical methods to solve the resulting differential equations. The team has a healthy portfolio of PhD positions and close collaborations with industrial partners. It consists of four full FTEs at Eindhoven University of Technology and one part-time professor.

The group has three research tracks: freeform design, imaging optics and improved direct methods; for more details see https://martijna.win.tue.nl/Optics/.

The text below does not contain figures due to restrictions in the application software system. Click here to see the full description as a PDF file.

The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. The surfaces are referred to as freeform since they do not have any symmetries. The governing equation for these problems is a nonlinear second-order partial differential equation (PDE) of Monge-Ampère type. The PDE is elliptic if we choose a positive right-hand side, it is hyperbolic for a negative one. The field of hyperbolic Monge-Ampère is relatively new. The elliptic cousin of the Monge-Ampère equation is well studied but on the hyperbolic case there are less results and hardly any publications on numerical methods to solve these problems. The elliptic PDE leads to convex or concave solutions, the hyperbolic one to saddle-shaped surfaces.

To design smooth periodic lens arrays, we need to combine concave, convex and saddle-shaped solutions. The research project aims to find solutions to the hyperbolic Monge-Ampère equation and to combine solutions into periodic surfaces.

Job Requirements
We are looking for talented enthusiastic PhD candidates who meet the following requirements:

• A master’s degree in (applied) mathematics or (applied) physics with a background in mathematical modeling and scientific computing
• Experience with solving ordinary and partial differential equations numerically
• Experience with programming (C, C++, Python, Matlab or alike)
• Creative pro-active team player with good analytical skills
• A research-oriented attitude
• Ability to work in an interdisciplinary team and interested in collaborating with industrial partners
• Motivated to develop your teaching skills and coach students
• Fluent in spoken and written English (C1 level)

Conditions of Employment
A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 - max. € 3,881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

About us
Eindhoven University of Technology is a leading international university within the Brainport region where scientific curiosity meets a hands-on mindset. We work in an open and collaborative way with high-tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact — today and in the future. TU/e is home to over 13,000 students and more than 7,000 staff, forming a diverse and vibrant academic community.

With over 110 (assistant, associate and full) professors, almost 300 PhD and EngD students, about 1.500 Bachelor students and 1000 Master students, the Department of Mathematics and Computer Science (M&CS) is the largest department of the TU/e. By performing top-level fundamental and applied research, and maintaining strong ties with industry, M&CS aims to contribute to science and innovation in and beyond the region.

Information
Do you recognize yourself in this profile and would you like to know more? Please contact the hiring manager dr.ir. Martijn Anthonissen, m.j.h.anthonissen@tue.nl.

Visit our website for more information about the application process or the conditions of employment. You can also contact HRServices.MCS@tue.nl.

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video.

Are you inspired and would like to know more about working at TU/e? Please visit our career page.

Application
We invite you to submit a complete application by using the apply button. The application should include a:

• Cover letter in which you describe your motivation and qualifications for the position.
• Curriculum vitae, including a list of your publications and the contact information of three references. Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.

Ensure that you submit all the requested application documents. We give priority to complete applications.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post.
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check, please consult the National Knowledge Security Guidelines.
• Please do not contact us for unsolicited services.

PhD position on computational illumination optics

The Computational Illumination Optics group is one of the few mathematics groups worldwide working on mathematical models of optical systems. They develop and analyze numerical methods to solve the resulting differential equations. The team has a healthy portfolio of PhD positions and close collaborations with industrial partners. It consists of four full FTEs at Eindhoven University of Technology and one part-time professor.

The group has three research tracks: freeform design, imaging optics and improved direct methods; for more details see https://martijna.win.tue.nl/Optics/.

The text below does not contain figures due to restrictions in the application software system. Click here to see the full description as a PDF file.

The goal in freeform design is to compute the shapes of optical surfaces (reflector/lens) that convert a given source distribution, typically LED, into a desired target distribution. The surfaces are referred to as freeform since they do not have any symmetries. The governing equation for these problems is a nonlinear second-order partial differential equation (PDE) of Monge-Ampère type. The PDE is elliptic if we choose a positive right-hand side, it is hyperbolic for a negative one. The field of hyperbolic Monge-Ampère is relatively new. The elliptic cousin of the Monge-Ampère equation is well studied but on the hyperbolic case there are less results and hardly any publications on numerical methods to solve these problems. The elliptic PDE leads to convex or concave solutions, the hyperbolic one to saddle-shaped surfaces.

To design smooth periodic lens arrays, we need to combine concave, convex and saddle-shaped solutions. The research project aims to find solutions to the hyperbolic Monge-Ampère equation and to combine solutions into periodic surfaces.

PhD in Patient-specific estimation of local variation of intraluminal thrombus properties in AAAs

Introduction

• Are you fascinated by cardiovascular biomechanics and its application to medical decision support?
• Are you eager to be trained to develop multi-level thrombosis risk prediction models by integrating cell-, thrombus-, and organ-level insights?
• Are you passionate about being part of a prestigious MSCA doctoral network working on revolutionizing personalized medicine through cutting-edge in silico, in vitro, and in vivo technologies to understand, predict and treat thrombosis?

Job Description
At the faculty of Biomedical Engineering at Eindhoven University of Technology, a PhD-position is available within the Thromborisk project, a Marie Sklodowska-Curie Actions (MSCA) Doctoral Network funded by the EU. The position is open for appointment during the course of 2026-2030, with a duration of 48 months hosted by TU/e, and includes secondments at the partner institutes within the consortium for a cumulative period of 12 months.

As a doctoral candidate (DC), you will be embedded in the Photoacoustics and Ultrasound Laboratory (PULS/e), a multidisciplinary and international team working on cutting-edge ultrasound and photoacoustic imaging technologies, image reconstruction, and model-based interpretation. Within this dynamic environment, you will collaborate closely with partners in the ThromboRisk Doctoral Network, participate in secondments at leading research institutes, and supervise BSc/MSc students on related projects.

Your main challenge will be to develop ultrasound-based methods to estimate patient-specific, spatially varying mechanical properties of intraluminal thrombus in abdominal aortic aneurysms. This involves combining advanced imaging techniques with biomechanical modeling to improve rupture risk prediction and support personalized clinical decision-making.

This position offers the opportunity to contribute to research with high societal impact: improving patient outcomes and reducing adverse events through better aneurysm risk assessment.

Research Programme Description
ThromboRisk – European Doctoral Network From cells to systems: Pioneering multi-level thrombosis risk prediction models consortium is funded by the European Union under Grant Agreement No. 101227706. It groups 10 hiring universities: Eindhoven University of Technology (NL), University of Maastricht (NL), University of Amsterdam (NL), Catholic University Leuven (BE), Charité – Universitätsmedizin Berlin (DE), University College London (UK), Transsilvania University of Brasov (RO), SANO Centre for Computational Personalized Medicine (PL), University of Leeds (UK), and University of Bern (CH).

ThromboRisk will develop an integrated platform to advance our understanding of thrombosis across biological scales, combining mechanobiology, biochemistry, pathophysiology, and computational modelling. For this inclusion to occur, each DC will develop through their research a unique contribution to the multi-level thrombosis risk prediction framework, addressing specific aspects of thrombus formation, growth, rupture, and clinical impact. This hands-on training is supplemented with several scientific professional courses and an immersive training program where the DCs can fine-tune their skills for the jobs of tomorrow, while addressing the societal challenges of the ThromboRisk program.

Job Requirements
We are looking for a candidate who meets the following requirements:

• You are creative and ambitious, hard-working, and persistent.
• You have a MSc degree in Biomedical Engineering, Electrical Engineering, Physics, or any other relevant program.
• You have theoretical and applied knowledge or interest in biomechanical and numerical modelling, and preferably also AI.
• You have a research-oriented attitude
• You have good communicative skills, and the attitude to partake successfully in the work of a research team.
• You have the ability to work in an interdisciplinary team and interested in collaborating with industrial partners.
• You are motivated to develop your teaching skills and coach students.
• You have a good command of the English language (Spoken and Written, Proficiency C1).

Conditions of Employment
A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 - max. € 3,881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

About us
Eindhoven University of Technology is a leading international university within the Brainport region where scientific curiosity meets a hands-on mindset. We work in an open and collaborative way with high-tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact — today and in the future. TU/e is home to over 13,000 students and more than 7,000 staff, forming a diverse and vibrant academic community.

The Department of Biomedical Engineering offers top-level education and research in one of the most relevant and exciting scientific disciplines of the 21st century: engineering health. In combining engineering and life sciences, through challenge-based learning and a multidisciplinary approach in collaboration with hospitals, industry and others, the department addresses the great challenges of the future, striving to improve healthcare and society as a whole.

Information
Do you recognize yourself in this profile and would you like to know more? Please contact the hiring manager Prof. Richard Lopata (r.lopata@tue.nl).

Visit our website for more information about the application process or the conditions of employment. You can also contact Sascha Sanchez van Oort, HR Advisor, s.j.m.g.sanchez.van.oort@tue.nl.

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video.

Are you inspired and would like to know more about working at TU/e? Please visit our career page.

Application
We invite you to submit a complete application by using the apply button. The application should include a:

• a cover letter in which you describe your motivation and qualifications for the position, including the topic of your MSc thesis project.
• a curriculum vitae (including contact details of at least three references). Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.
• a list of BSc and MSc courses and grades.

Ensure that you submit all the requested application documents. We give priority to complete applications.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post.
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check, please consult the National Knowledge Security Guidelines.
• Please do not contact us for unsolicited services.