Internship | What is the utility of scientific machine learning for the modelling of engineering structures?

Combine the power of physics and data-driven approaches for a new generation of modelling of engineering structures.



Education type

university (wo)


Internship and graduation project

Hours a week

Fulltime – 40


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What will you be doing?

One of the main enterprises of science and engineering is the modelling of physical systems. There is a perpetual quest for “better” models, i.e. models with higher predictive accuracy and based on fewer and more fundamental principles. Models that can provide more insight and enable more economic design and management of systems.
At present, computational physics models, such as finite element models, are the dominant models in engineering; however, in some cases they have considerable limitations (see below). A promising novel approach to overcome these limitations is to combine physics with machine learning: scientific machine learning (SciML) [1-3]. The goal of this MSc thesis is to explore the utility of SciML in the field of structural engineering through a real-world case.
The current computational physics based modelling
  • relies on manual model development and manual refinement of model parameters;
  • requires well-posed models/problems for solvability and does not allow for leaving certain aspects open -- although they might be unknown or uncertain -- to be learned from measurements, e.g. boundary conditions;
  • is a labor intensive and time consuming process that prohibits the creation of models in mass, e.g. for each individual asset such as wind turbines in a wind farm;
  • is not “friendly” to the inflow of a large amount of measurement data, although it is becoming ever cheaper, omnipresent, and carries valuable information about the measured system.
SciML has the potential to overcome all of the above limitations. The basic idea of SciML is to incorporate information from (1) theories, e.g. laws of physics, and from (2) measurements as well (see Figure 1). If sufficient data is available it offers the possibility to “learn” a phenomenon which is not explicitly included in the model, e.g. friction at supports where the base model (e.g. computational physics model) neglects frictional forces. In a recent paper the approach was described as “a potentially transformative technology” and “a new paradigm in modelling and computation” [1]. We share this positivism regarding the potential of the approach.

You will
  • continue the work of TNO researchers;
  • work closely with experts in computational physics, structural reliability, and machine learning at TNO;
  • review the most recent literature on SciML;
  • explore various model formulations: between the leftmost and rightmost parts of the scale illustrated in Figure 1;
  • devise novel SciML formulations, e.g. discrepancy modelling, enforcing boundary conditions, enforcing differential equations, etc.;
  • implement SciML formulations in a selected machine learning framework, Julia and Flux are preferred;
  • perform SciML based modelling using real measurements and compare the results with purely data-driven and “purely” physics(theory)-driven approaches;
  • explore how the uncertainty of the SciML model predictions can be quantified;
  • learn how to perform, document, and present your own research.
Conditional on good progress, we expect to publish one international journal paper based on the results of the MSc thesis. Your work will be embedded into an ongoing research project at TNO and you will jointly work with TNO researchers rather than left alone with your topic.

What do we require of you?

  • You are following a master program in Civil Engineering, Mechanical Engineering, Aerospace Engineering, Computational Science, Computer Science, or any related fields;
  • You have at least three of these skills (feel free to apply if you only have two of them but you are confident that you will pick up the rest);
  • You have at least a basic knowledge on continuum mechanics and numerical approaches to solve continuum mechanics problems, e.g. finite element method, and finite difference method;
  • You are familiar with the basics of machine learning, e.g. neural networks, cross-validation. You have fitted and evaluated at least one neural network and you are familiar with the basic concepts such as activation function, fully connected layers, loss function, and automated differentiation;
  • You are familiar with numerical analysis concepts and algorithms, e.g. optimization (convex, gradient-based, gradient-free, constrained, etc.), linear algebra, solving differential equations, and solving system of nonlinear equations;
  • You have demonstrated skills in at least one computer language, preferably with a focus on numerical computation, e.g. Python, Matlab, Julia, or R. Julia is preferred;
  • You are proactive and eager to learn new concepts and develop new skills.

What can you expect of your work situation?

TNO is an independent research organisation whose expertise and research make an important contribution to the competitiveness of companies and organisations, to the economy and to the quality of society as a whole. Innovation with purpose is what TNO stands for. With 3000 people we develop knowledge not for its own sake but for practical application. To create new products that make life more pleasant and valuable and help companies innovate. To find creative answers to the questions posed by society. We work for a variety of customers: governments, the SME sector, large companies, service providers and non-governmental organisations. Working together on new knowledge, better products and clear recommendations for policy and processes. In everything we do, impact is the key. Our product and process innovations and recommendations are only worth something if our customers can use them to boost their competitiveness.

What can TNO offer you?

You want to work on the precursor of your career; a work placement gives you an opportunity to take a good look at your prospective future employer. TNO goes a step further. It’s not just looking that interests us; you and your knowledge are essential to our innovation. That’s why we attach a great deal of value to your personal and professional development. You will, of course, be properly supervised during your work placement and be given the scope for you to get the best out of yourself. Naturally, we provide suitable work placement compensation.

Has this vacancy sparked your interest?

Then please feel free to apply on this vacancy! For further questions don’t hesitate to contact us.

Contact: Arpad Rozsas
Phone number: +31615138029

Ongeldige gegevens (NotSupported)

Note that applications via email and third party applications are not taken into consideration.


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