It is time to sort out the zoo of methods that has emerged in the field of Deep Learning in Computational Mechanics [1,2]. To this end, I will give a very short methodological classification and try to identify core properties of research directions in this field which we think have potential.

I will then demonstrate an interesting property of neural networks that is not well understood but which enables them to find better local minima in optimization problems [3].

The presentation will finish with an outlook of what might happen when the bubble bursts: Millions of unused graphics cards that can perform matrix vector computations with astonishing efficiency [4].


REFERENCES
[1] L. Herrmann and S. Kollmannsberger, „Deep Learning in Computational Mechanics: a review“, Computational Mechchanics, Bd. 74, Nr. 2, S. 281–331, Aug. 2024, doi: 10.1007/s00466-023-02434-4.
[2] http://www.deeplearningincomputationalmechanics.com
[3] L. Herrmann, O. Sigmund, V. M. Li, C. Vogl, und S. Kollmannsberger, „On Neural Networks for Generating Better Local Optima in Topology Optimization“, Structural Multidisciplinary Optimization, Bd. 67, Nr. 11, S. 192, Nov. 2024, doi: 10.1007/s00158-024-03908-6.
[4] L. Herrmann, T. Bürchner, L. Kudela, and S. Kollmannsberger, „A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems“, 19. September 2025, arXiv: arXiv:2509.15744. doi: 10.48550/arXiv.2509.15744.