Topology Optimization in Fluid Applications

The goal is to understand, compare, and enhance classical approaches and approaches based on machine learning techniques to solve topology optimization in fluid applications.

Shape and topology optimization is an interdisciplinary research field in applied mathematics and engineering. It is concerned with finding the optimal shape or design. Applications are manifold and include the optimization of electrical motors and cooling devices. Therefore, shape and topology optimization has the potential to address essential societal and industrial questions. In order to be able to address real-world applications in a robust and reliable manner, existing methods have to be enhanced.


Recently, machine learning approaches were applied to topology optimization. We want to find out to which extend the proposed approaches have the potential to enhance and outperform classical methods. To do so, we build on two recent papers and extend the results to more advanced---yet still academic toy---examples for topology optimization of fluids.

Learning outcome

In the scope of the thesis the student will learn how to use FEniCS and PyTorch to solve topology optimization problems in fluid applications. Moreover, the student will understand classical and machine learning based approaches for topology optimization.


A background in applied mathematics, mechanics, and/or computer science is required. Knowledge of partial differential equations, numerical methods such as finite element methods, and/or high-level programming is a must. Knowledge of functional analysis, mathematical optimization and/or machine learning is a plus.


  • Henrik Nicolay Finsberg
  • Johannes Haubner

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