NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
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发表时间：
2019-08
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通讯作者：
Yifan Sun;Linan Zhang;Hayden Schaeffer
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作者：
Yifan Sun;Linan Zhang;Hayden Schaeffer
我们提出了一种基于神经网络的方法，从动态数据中提取模型，使用普通和偏微分方程。特别是，给定一个时间序列或时空数据集，我们试图确定一个精确的管理系统，尊重内在的差分结构。未知的管理模型参数化，通过使用（浅）多层感知器和非线性微分项，以纳入时空样本之间的相关性。我们展示了几个例子中的数据是从各种动力系统采样的方法，并给出了比较经常性的网络和其他数据发现方法。此外，我们还表明，对于MNIST和Fashion MNIST，与其他深度神经网络相比，我们的方法降低了参数成本。
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing system which respects the intrinsic differential structure. The unknown governing model is parameterized by using both (shallow) multilayer perceptrons and nonlinear differential terms, in order to incorporate relevant correlations between spatio-temporal samples. We demonstrate the approach on several examples where the data is sampled from various dynamical systems and give a comparison to recurrent networks and other data-discovery methods. In addition, we show that for MNIST and Fashion MNIST, our approach lowers the parameter cost as compared to other deep neural networks.