Flanders Make

Automated physical laws discovery in noisy measurement data using a deep learning technique to solve industrial problems

Flanders Make

Flanders Make is the strategic research centre for the manufacturing industry. Our mission is to strengthen the long-term international competitiveness of the Flemish manufacturing industry. That’s why we work together with SMEs and large companies on pre-competitive, industry-driven technological research, resulting in concrete product and production innovation in the vehicle industry, the manufacturing industry, and production environments.

Goal of the internship

A lot of efforts have been made these days to combine data-driven science with bottom-up physical modelling in a new field known as "physics-guided data science". Integration of first-principle models with data science techniques has already proven successful results in various applications including, material science, earth science and fluid mechanics. The so-called Physics-Informed Neural Networks (PINNs) which follows this approach has proven useful to retrieve coefficients of known PDEs from artificial data, and even to directly discover physical models from artificial data, i.e., PDE-NET, PDE-Stride and PDE-Find.

The problem of data-driven model discovery of PDEs has been approached from several different directions. An alternative approach recently proposed in the literature is to use sparse regression model selection schemes such as PDE-FIND to discover a PDE from a spatial-temporal dataset. In this approach, the PDE underlying a dataset u({x, t}) is discovered by writing the model discovery task as a regression problem where we are trying to estimate the coefficients of the PDE. This leverages the automatic differentiation capabilities of deep learning frameworks, originally intended for their backpropagation-based training. By learning how to calculate various order derivatives with respect to time and/or space, this approach makes it possible to explicitly model the relationship between said derivatives and the system dynamics. The sparseness of the regression technique helps us deal with the large number of possible models by setting many PDE coefficients to zero, excluding them from the resulting model. Examples of such automated techniques include Deep Hidden Physics Models (DHPM), and DeepMoD.

The Flanders Make team has recently gained some experience in applying one of these techniques to some industrial applications with promising results. However, when the measurement data is noisy, the selected technique seems to perform sub-optimally. Hence, further exploitation and exploration of these techniques are necessary to understand the limitation and the applicability towards real-industrial problems.

The goals of this internship are 1) to further explore the recently developed physics-guided deep learning methods to automatically discover the partial differential equation (PDE) from underlying noisy measurement data set, 2) to demonstrate their performances, and 3) to assemble the required libraries into an easy-to-use, flexible, Pythonic format where necessary.

Learning target: The student will learn to

  1. Deal with exploratory ML research, particularly deep learning;
  2. Replicate and/or survey the state-of-the-art in ML;
  3. Re-formulate physics problems as ML problems;
  4. Implement and validate the selected ML technique to solve real-industrial problems.

Profile Student

  • Bachelor degree in Computer science, Artificial Intelligence, electronics, control or mechatronic engineering;
  • (Some) Knowledge of Python programming and artificial intelligence is highly recommended
  • Knowledge on physical modelling and system identification, and/or experience with Matlab/Simulink is an advantage;
  • Passionate by research and new technologies with focus on applications for machines or mechatronic systems of the companies;
  • Result oriented, responsible and proactive;
  • A good communicator, able to communicate in English;
  • Eager to learn and a team player.

Only EEA (or Swiss) nationals can be accepted for internships due to work permit regulations.

Practical Data

  • Internship: The assignment is for an internship of min. 4 months to maximum 6 months and takes place at the offices of Flanders Make located in Leuven, Belgium.
  • Thesis: This assignment is also a possible topic for a master thesis for a Belgian university.


  • Locatie: Gaston Geenslaan 8, 3001 Leuven


Voor meer informatie:
op het nummer: +32 16 910 614 (Ma-di-woe-do: 9u-16u)
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