Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
Center for Applied Mathematics, Cornell University, Ithaca, NY, 14853, USA.
Sci Rep. 2022 Mar 22;12(1):4824. doi: 10.1038/s41598-022-08745-5.
There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. To do this, we develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses under excitations drawn from a Gaussian process, we train rational neural networks to learn Green's functions of hidden linear partial differential equations. These functions reveal human-understandable properties and features, such as linear conservation laws and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate the technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity.
深度学习有机会通过以人类可理解的方式揭示其发现来彻底改变科学和技术。为此，我们开发了一种新颖的数据驱动方法来创建人机合作伙伴关系，以加速科学发现。通过在从高斯过程中得出的激励下收集物理系统的响应，我们训练理性神经网络来学习隐藏线性偏微分方程的格林函数。这些函数揭示了人类可理解的属性和特征，例如线性守恒定律和对称性，以及冲击波和奇点位置、边界效应和主导模式。我们在几个例子上演示了该技术，并捕获了包括对流扩散、粘性冲击波和驱动盖腔中的斯托克斯流在内的一系列物理现象。
