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.
翻译:机器学习(ML)技术的应用,特别是神经网络的应用,在处理图像和语言方面都取得了巨大成功。这是因为我们常常缺乏理解视觉和音频输入的正式模型,因此这里神经网络可以展示它们的能力,因为它们只能用数据做模型。在物理学领域,我们通常有模型,在正式的层次上对自然过程描述得相当好。不过,近年来,ML也证明在这些领域有用,不管是加速数字模拟还是提高精确度。古典物理学中的一个重要和迄今尚未解决的问题是理解动荡流运动。在这项工作中,我们通过使用Gledzer-Ohkitani-Yamada(GOY)型贝壳模型来构建一个非常简化的波动代表。我们打算利用这个系统来调查ML支持的和物理上受限制的小规模动荡模型的潜力。我们不是在标准监督下学习,而是提出一种旨在重建波动统计特性的方法,例如自我相似的惯性测幅度测量,我们可以在那里取得鼓励实验结果。此外,我们讨论在将机器学习与差异方程式相结合时的误差。