Neural partial differential equations for chaotic systems
Neural partial differential equations for chaotic systems
复制标题
混沌系统的神经偏微分方程
DOI：
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复制
发表时间：
2021
影响因子：
3.3
通讯作者：
J. Kurths
中科院分区：
文献类型：
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作者：
Maximilian Gelbrecht;N. Boers;J. Kurths
当预测复杂系统时，人们通常依赖于微分方程，微分方程通常是不完整的，缺少未知的影响或高阶效应。通过用人工神经网络扩充方程，我们可以弥补这些不足。我们表明，这可以用来预测范式，高维混沌偏微分方程，即使只有短期和不完整的数据集。这些高维系统的预测范围大约比训练数据的长度大一个数量级。
When predicting complex systems one typically relies on differential equation which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.