壳模型湍流模拟的自动耗散控制
Automated Dissipation Control for Turbulence Simulation with Shell Models
摘要：
机器学习（ML）技术的应用，特别是神经网络，在处理图像和语言方面取得了巨大的成功。这是因为我们通常缺乏正式的模型来理解视觉和音频输入，所以这里神经网络可以展现它们的能力，因为它们可以单独从数据建模。在物理学领域，我们通常有模型，在形式层面上合理地描述自然过程。尽管如此，近年来，ML在这些领域也被证明是有用的，无论是通过加速数值模拟还是通过提高准确性。在经典物理学中，一个重要而至今尚未解决的问题是理解湍流运动。在这项工作中，我们构造了一个强烈简化的湍流表示使用Gledzer-Ohkitani-Yamada（GOY）壳模型。有了这个系统，我们打算调查ML支持和物理约束的小尺度湍流建模的潜力。而不是标准的监督学习，我们提出了一种方法，旨在重建湍流的统计特性，如自相似惯性范围缩放，在那里我们可以取得令人鼓舞的实验结果。此外，我们还讨论了将机器学习与微分方程相结合时的陷阱。
英文摘要：
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.
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