Internship | Physics-informed machine learning for more accurate 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


Apply now


What will you be doing?

What is the challenge?

One of the main enterprises of science and engineering is the modelling of physical systems. There is a perpetual quest for “better” models, e.g. 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. The current computational physics based modelling
  • relies on manual model development and manual refinement of 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 labour 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 and omnipresent and carries valuable information about the measured system.

The goal of this MSc thesis project is to explore a novel approach: physics-informed machine learning (PIML) [1-4] that has the potential to overcome the above challenges. The aim of the project is to deliver a proof of concept study (potentially moving towards piloting) on the added value of physics-informed machine learning on a selected structural engineering application.

The basic idea of PIML is that it incorporates information from (1) theories, e.g. laws of physics, and from (2) measurements as well (see the image below). 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.

PIML is agnostic to geometry, boundary conditions, and physical properties, it can learn these from the collected data in an automated fashion [2-3]. Hence there is no need for tedious, hand-crafted models for each asset; even more, the physics-informed machine learning model is expected to be more accurate than traditional computational physics based models as it continuously learns from the collected data and incorporates them into the model.

In a recent paper [1] physics-informed machine learning was described as “a potentially transformative technology” and “a new paradigm in modelling and computation”. We share this positivism regarding the potential of the approach.

What will you do?
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 PIML;
  • explore various model formulations: between the leftmost and rightmost parts of the scale illustrated in image below.
  • devise novel PIML formulations, e.g. discrepancy modelling, enforcing boundary conditions, enforcing differential equations, etc.;
  • implement PIML formulations in a selected machine learning framework, e.g. TensorFlow, PyTorch.
  • perform PIML using real measurements and compare the results with purely data-driven and “purely” physics(theory)-driven approaches;
  • explore how the uncertainty of the PIML 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.

What do we require of you?

You are following a master program in Civil Engineering, Mechanical Engineering, Aerospace Engineering, Computational Science, Computer Science, Applied Physics, Applied Mathematics or any related fields.

You have at least three of these skills:
  • 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 trained 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. Python is preferred.
  • You are proactive and eager to learn new concepts and develop new skills.

## References
[1] M. Raissi, P. Perdikaris, G.E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics, 378 (2019), p. 686-707,
[2] M. Raissi, G.E. Karniadakis, Hidden physics models: machine learning of nonlinear partial differential equations, 2017, arXiv:1708 .00588.
[3] M. Raissi, Perdikaris P., G.E. Karniadakis, Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations, 2017, arXiv:1711.10561.
[4] D.C. Psichogios, L.H. Ungar, A hybrid neural network-first principles approach to process modeling, AIChE J. 38 (1992), p. 1499–1511.

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, 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.

Schematic, high-level overview of the thesis topic

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.

Due to Covid-19 and the consequent uncertainties and restrictions, students who are not residing in the Netherlands may currently not be able to start an internship or graduation project at TNO.

Contact: Arpad Rozsas
Phone number: +31(0)615138029

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


Apply now



Stay up to date with our latest news, activities and vacancies collects and processes data in accordance with the applicable privacy regulations for an optimal user experience and marketing practices.
This data can easily be removed from your temporary profile page at any time.
You can also view our privacy statement or cookie statement.