The application of machine learning (ML) techniques, especially neural
networks, has seen tremendous success at processing images and language. This
is because we often lack formal models to understand visual and audio input, so
here neural networks can unfold their abilities as they can model solely from
data. In the field of physics we typically have models that describe natural
processes reasonably well on a formal level. Nonetheless, in recent years, ML
has also proven useful in these realms, be it by speeding up numerical
simulations or by improving accuracy. One important and so far unsolved problem
in classical physics is understanding turbulent fluid motion. In this work we
construct a strongly simplified representation of turbulence by using the
Gledzer-Ohkitani-Yamada (GOY) shell model. With this system we intend to
investigate the potential of ML-supported and physics-constrained small-scale
turbulence modelling. Instead of standard supervised learning we propose an
approach that aims to reconstruct statistical properties of turbulence such as
the self-similar inertial-range scaling, where we could achieve encouraging
experimental results. Furthermore we discuss pitfalls when combining machine
learning with differential equations.

通过使用 Gledzer-Ohkitani-Yamada (GOY) shell 模型的强烈简化表示，我们构建了一个小尺度湍流模型进行研究，重点探讨了机器学习与物理学的相结合，以及在将机器学习与微分方程相结合时存在的问题。