2026 - T2 - WS3 - Idealised mathematical models for geophysical flows

Collection 2026 - T2 - WS3 - Idealised mathematical models for geophysical flows

Organizer(s) Dormy, Emmanuel ; Lacave, Christophe ; Oruba, Ludivine ; Vasseur, Alexis
Date(s) 29/06/2026 - 03/07/2026
linked URL https://indico.math.cnrs.fr/event/13870/
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Thoughts on Machine Learning

By Rupert Klein

Techniques of machine learning (ML) find a rapidly increasing range of applications touching upon many aspects of everyday life. They are also used with enthusiasm to close gaps in our scientific knowledge by data-based modeling. I have followed these developments with interest, concern, and mounting disappointment. When these technologies take over decisive functionality in safety-critical applications, we should know how to guarantee their compliance with pre-defined guardrails. Moreover, when they are utilized as building blocks in scientific research, it would violate scientific standards if these building blocks were used without a thorough understanding of their functionality, including inaccuracies, uncertainties, and other pitfalls. In this context, I will juxtapose (a subset of) deep neural network methods with the family of entropy-optimal ML techniques developed recently by Illia Horenko (RPTU Kaiserslautern-Landau) and colleagues.

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  • Y.-G. Ham, J.-H. Kim, J.-J. Luo, Deep learning for multi-year ENSO forecasts, Nature, 573:7775, 568–572 (2019).
  • J. He, L. Li, J. Xu, Ch. Zheng, ReLU deep neural networks and linear finite elements, J. Comput. Math., 38:3, 502–527 (2020).
  • J. Siegel, J. Xu, Approximation rates for neural networks with general activation functions, Neural Net- works, 128, 313–321 (2020).
  • E. Vecchi, L. Pospisil, S. Albrecht, T.J. O’Kane, I. Horenko, Scalable Entropy-Optimal Machine Learning Classification for Small Data Problems, Neural Comput., 34:5, 1220–1255 (2022).
  • I. Horenko, On existence, uniqueness and scalability of adversarial robustness and control measures for AI classifiers; arXiv:2310.14421 (2023).

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