ECCOMAS 2024

Keynote

On the applicability and usefulness of AI in Topology Optimisation

  • Woldseth, Rebekka Vaarum (Technical University of Denmark)
  • Aage, Niels (Technical University of Denmark)
  • Bærentzen, Jakob Andreas (Technical University of Denmark)
  • Sigmund, Ole (Technical University of Denmark)

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The portfolio of Artificial Intelligence based applications for improving the computational efficiency and solution quality trade-off in Topology Optimisation (TO) and other inverse problems is continuously expanding. Most of these applications, however, suffer from inherent deficiencies in that they are based on Neural Networks (NNs) that require an extensive number of examples for training yet produce low quality solutions, in some cases even for problems closely resembling the training data [1]. Other applications rely on reducing the model complexity, which generally reduces the length-scale control and obtained detail in the TO results. The nature of a good quality TO solution is dependent upon the physics governing the optimisation problem, and the finite element computation performed at each iteration in the conventional TO approach is what predominantly contributes to the extensive computational cost associated with optimising large-scale problems [2]. Incorporating these characteristics into any AI-based methodology will also increase the cost of developing and applying such methods significantly. Therefore, the most promising types of applications of NNs in TO are focused on solving specific sub-tasks that preferably can be isolated from the governing physics [1]. One such application is aimed at utilising a pre-trained NN to perform the mapping from a homogenisation-based multiscale result to a single-scale structure [3]. The homogenised optimisation result considered, represents a set of lamination layers described by their orientations and thicknesses on a coarse mesh. Dehomogenisation then denotes the procedure of translating each of these layers to a fine-resolution periodic field with smooth transitions between the spatially prescribed orientations and thicknesses from the input optimised solution and combine them to obtain a final single-scale structure. This procedure more closely resembles image- or pattern-related problems for which AI-applications have proven fruitful. Training a NN to perform this task does, however, come with several challenges related to conflicts between conformality and periodicity causing bifurcations. During investigations of how to overcome these challenges other computer graphics related disciplines such as procedural noise functions have emerged as promising alternatives, where especially Phasor Noise offers a similar computational efficiency but with better control and structural integrity [4].