Forecasting the behaviour of complex dynamical systems such as interconnected sensor networks characterized by high-dimensional multivariate time series(MTS) is of paramount importance for making informed decisions and planning for the future in a broad spectrum of applications. Graph forecasting networks(GFNs) are well-suited for forecasting MTS data that exhibit spatio-temporal dependencies. However, most prior works of GFN-based methods on MTS forecasting rely on domain-expertise to model the nonlinear dynamics of the system, but neglect the potential to leverage the inherent relational-structural dependencies among time series variables underlying MTS data. On the other hand, contemporary works attempt to infer the relational structure of the complex dependencies between the variables and simultaneously learn the nonlinear dynamics of the interconnected system but neglect the possibility of incorporating domain-specific prior knowledge to improve forecast accuracy. To this end, we propose a hybrid architecture that combines explicit prior knowledge with implicit knowledge of the relational structure within the MTS data. It jointly learns intra-series temporal dependencies and inter-series spatial dependencies by encoding time-conditioned structural spatio-temporal inductive biases to provide more accurate and reliable forecasts. It also models the time-varying uncertainty of the multi-horizon forecasts to support decision-making by providing estimates of prediction uncertainty. The proposed architecture has shown promising results on multiple benchmark datasets and outperforms state-of-the-art forecasting methods by a significant margin. We report and discuss the ablation studies to validate our forecasting architecture.

翻译：预测复杂动态系统（如以高维多变量时间序列为特征的互连传感器网络）的行为，对于在广泛的应用领域中做出明智决策和规划未来至关重要。图预测网络非常适合预测具有时空依赖性的多变量时间序列数据。然而，先前大多数基于图预测网络的多变量时间序列预测方法依赖于领域专业知识来建模系统的非线性动力学，却忽略了利用多变量时间序列数据中时间序列变量之间固有的关系-结构依赖性的潜力。另一方面，现有研究尝试推断变量间复杂依赖关系的关系结构，并同时学习互连系统的非线性动力学，但忽视了融入领域特定先验知识以提高预测准确性的可能性。为此，我们提出了一种混合架构，将显式先验知识与多变量时间序列数据中关系结构的隐式知识相结合。该架构通过编码时间条件化的结构时空归纳偏置，联合学习序列内的时间依赖性和序列间的空间依赖性，以提供更准确可靠的预测。它还建模了多步预测的时变不确定性，通过提供预测不确定性的估计来支持决策制定。所提出的架构在多个基准数据集上显示出有希望的结果，并以显著优势优于最先进的预测方法。我们报告并讨论了消融研究以验证我们的预测架构。