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PhD position on physics-informed machine learning for smart materials

PhD position on physics-informed machine learning for smart materials

Mechanical Engineering


Smart materials promise unprecedented advances in their exotic properties and engineering applications. Scaling traditional models for such materials faces major challenges posed by the computationally intensive first-principle models. Recent advances in hybrid approaches of physics-informed machine learning offer a great opportunity to overcome existing challenges and deliver outstanding results. Join our multidisciplinary team of scientists from Mechanical Engineering and Computer Science on this exciting journey.

Job Description

We are looking for a highly creative and motivated PhD candidate to join the Mechanics of Materials section at the Eindhoven University of Technology (TU/e). The position is in the group led by Prof. Marc G.D. Geers and co-supervised by an interdisciplinary team of scientists Ondřej Rokoš (Mechanical Engineering), Vlado Menkovski (Mathematics & Computer Science), and Martin Doškář (CTU in Prague, Department of Mechanics).

Context. Metamaterials owe their name to their unprecedented effective behavior that typically cannot be found in Nature and that often combines contradictory properties, such as being ultra-stiff & ultra-light, or auxetic behavior. These properties usually emerge from the metamaterials’ complex micro-structural morphology rather than from the properties of individual material constituents. Recent trends in metamaterial design aim at their actuation using, e.g., pneumatic or magnetic means. Metamaterials thus offer a rich design space, which can be exploited in numerous applications such as artificial muscles, medical robotics, bio-implants, soft robotics, or self-folding systems.

Objective. The objective of this project is to develop Machine Learning based solutions for the design and optimal control of engineering-scale devices, manufactured from advanced/smart active metamaterials. Optimal control of such systems with many degrees of freedom necessitates real-time yet high-accuracy multiscale simulations to predict mechanical behavior relevant at the engineering scale, hierarchically emerging from the underlying microstructure.

Development of such materials usually relies on computationally intensive first-principle microstructural models, which need to be parameterized by typical microstructural features such as varying thermo-mechanical properties of the microstructural constituents, or coupling with external fields. This results in prohibitive computational complexity that limits the possibility to scale the development of smart materials to a broader range.

Machine learning technology, such as deep neural networks, has enabled major advancements in various fields, especially in high-dimensional setting. These methods usually deliver black-box models that require large amount of supervised data and do not efficiently benefit from the existing domain knowledge. Recent advances in incorporating physical knowledge, such as physical laws in Deep Learning Models, open a promising avenue for utilizing the rich domain knowledge available in Materials Science for development of smart materials.

In this multidisciplinary project we aim to advance the state of the art of both the fields of Materials Science and Machine Learning by developing new materials and methods for efficiently incorporating domain knowledge into Machine Learning models.

Implementation. To achieve this objective, the PhD project is planned to cover several aspects of multi-scale modeling of advanced metamaterials. (i) To alleviate the limitations of the computationally intensive first-principle microstructural models, reliable forward surrogates for the computation of the effective properties need to be constructed. (ii) To cover a large design space, these surrogates need to be parameterized by typical microstructural features. (iii) Their inversion will allow for efficient search of optimal microstructures with target engineering properties. (iv) Machine learning tools will be used to discover non-standard equations governing the resulting effective systems.

Exposition. During the execution phase of this project, you will be exposed to, gain understanding, and deepen your knowledge in concepts such as advanced machine learning tools (PyTorch, TensorFlow), neural networks, variational encoders, advanced first-principle nonlinear solid mechanics & multiphysics modeling, multiscale computational homogenization, finite elements, or optimization/topology optimization techniques.

Section Embedding. The research will be embedded within the section Mechanics of Materials (, whose activities concentrate on the fundamental understanding of various macroscopic problems in materials processing and forming, emerging from the physics and the mechanics of the underlying material microstructure. The main challenge is the accurate prediction of mechanical properties of materials with complex micro-structures, with a direct focus on industrial needs. The thorough understanding and modeling of ‘unit’ processes that can be identified in the complex evolving microstructure is thereby a key issue. The group has a unique research infrastructure, both from an experimental and computational perspective. The Multi-Scale Lab allows for quantitative in-situ microscopic measurements during deformation and mechanical characterization, and it constitutes the main source for all experimental research on various mechanical aspects of materials within the range of 10-9–10-2 m. In terms of computer facilities, several multi-processor-multi-core computer clusters are available, as well as a broad spectrum of in-house and commercial software.


Highly talented and enthusiastic candidates with excellent analytical skills and excellent grades are encouraged to apply. An MSc degree in Mathematics, Applied Mathematics, Computer Science, Mechanical Engineering, Physics, Materials Science, or a related discipline is required, as well as a strong background in computational methods. In particular, students with a specialization in machine learning, neural networks, micro-mechanics & multi-scale modelling, and finite element techniques are encouraged to apply. The ideal candidate has excellent scientific skills with a reserach-oriented attitude, outstanding verbal and written communication skills, and is fluent in spoken and written English.


  • A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
  • A full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months.
  • To develop your teaching skills, you will spend 10% of your employment on teaching tasks.
  • To support you during your PhD and to prepare you for the rest of your career, you will make a Training and Supervision plan and you will have free access to a personal development program for PhD students (PROOF program).
  • A gross monthly salary and benefits (such as a pension scheme, pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labor Agreement for Dutch Universities.
  • Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
  • Should you come from abroad and comply with certain conditions, you can make use of the so-called ‘30% facility’, which permits you not to pay tax on 30% of your salary.
  • A broad package of fringe benefits, including an excellent technical infrastructure, moving expenses, and savings schemes.
  • Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.

Informatie en sollicitatie

More information

Do you recognize yourself in this profile and would you like to know more?
Please contact dr. Ondřej Rokoš, o.rokos[at]

For information about terms of employment, please click here or contact HRadviceME[at]

Please visit to find out more about working at TU/e!


We invite you to submit a complete application by using the ‘apply now’ button on this page.
The application should include:

  • A cover letter in which you describe your motivation and qualification for this position.
  • Curriculum vitae, including a list of your publications and the contact information of
    three references.
  • A brief summary of your MSc thesis, highlighting your main contribution.
  • Transcripts of your BSc and MSc degrees (with grades).

Note that we do not respond to applications that are sent to us in a different way. Both national and international applications to this advertisement are appreciated.

We are looking forward to your application and will screen it as soon as we have received it. Screening will continue until the position has been filled. Promising candidates will be contacted by email.

Please keep in mind you can upload only 5 documents up to 2 MB each. If necessary please combine files.