DeepMoD：噪声数据中模型发现的深度学习
DeepMoD: Deep learning for Model Discovery in noisy data
摘要：
我们介绍DeepMoD，一种基于深度学习的模型发现算法。DeepMoD使用可能函数及其导数库的稀疏回归发现时空数据集背后的偏微分方程。神经网络近似数据并构建函数库，但它也执行稀疏回归。这种结构使得它对噪声非常鲁棒，适用于小数据集，并且与其他深度学习方法相反，它不需要训练集。我们基准我们的方法上的几个物理问题，如汉堡，Korteweg-de Vries和凯勒-西格尔方程，并发现它需要尽可能少的$\mathcal{O}(10^2)$样本和工作在噪音水平高达$75\%$。受这些结果的启发，我们将DeepMoD直接应用于凝胶电泳实验的噪声实验时间序列数据，发现它发现了描述该系统的对流扩散方程。
英文摘要：
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, but it also performs the sparse regression. This construction makes it extremely robust to noise, applicable to small data sets, and, contrary to other deep learning methods, does not require a training set. We benchmark our approach on several physical problems such as the Burgers', Korteweg-de Vries and Keller-Segel equations, and find that it requires as few as $\mathcal{O}(10^2)$ samples and works at noise levels up to $75\%$. Motivated by these results, we apply DeepMoD directly on noisy experimental time-series data from a gel electrophoresis experiment and find that it discovers the advection-diffusion equation describing this system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
