McDermott Patrick L, Wikle Christopher K
Jupiter Intelligence, Boulder, CO 80302, USA.
Department of Statistics, University of Missouri, Columbia, MO 65211, USA.
Entropy (Basel). 2019 Feb 15;21(2):184. doi: 10.3390/e21020184.
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. Recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications.
循环神经网络（RNNs）是非线性动力学模型，常用于机器学习和动力学系统文献中，以表示变量之间复杂的动力学或序列关系。最近，随着深度学习模型变得越来越普遍，RNNs已被用于预测日益复杂的系统。动态时空过程代表了一类复杂系统，这类系统可能会从这些类型的模型中受益。尽管RNN的文献非常丰富且高度发达，但不确定性量化往往被忽视。即使考虑到不确定性，通常也在没有使用严格框架（如完全贝叶斯设置）的情况下进行量化。在这里，我们试图在一个更正式的框架中量化不确定性，同时保持使这些模型具有吸引力的预测准确性，为此我们提出了一种用于非线性时空预测的贝叶斯RNN模型。此外，我们对基本的RNN进行了简单修改，以帮助适应非线性时空数据的独特性质。所提出的模型应用于洛伦兹模拟和两个实际的非线性时空预测应用。
