在大数据时代，数据的积累和分析已经成为解决各种问题和挖掘价值的重要手段。在许多实际场景中，我们不仅仅对数据之间的相关性感兴趣，更希望能够理解变量之间的格兰杰因果关系。这种因果关系可以帮助我们预测未来情况、识别影响因素以及设计有效的干预措施。现有的格兰杰因果关系推断模型的大多数都假设线性动力学，然而现实世界中的绝大多数相互作用却是非线性的。在这些情况下，将线性因果模型用在非线性时间序列上会导致错误的格兰杰因果推断。

应用深度学习可以很好的改善上述问题，一方面，神经网络的非线性特性使其能够更好地捕捉多维时间序列中复杂的因果关系。另一方面，通过将深度学习与Lasso惩罚相结合可以自动推断格兰杰因果的时间滞后，而无需像线性模型一样手动选择滞后，进一步的提高了因果推断能力。因此，本文通过将深度学习和Lasso惩罚相结合，提出两个基于深度学习的格兰杰因果推理模型GC-Mixer和GC-LSTM，可从多维时间序列的中提取格兰杰因果关系并自动推断时间滞后，主要研究和工作内容如下：

（1）提出了因果推理模型GC-Mixer，使用了多个堆叠的MLP混合块分别提取序列的时间和空间特征，并推断多维时间序列间的因果关系。相比于传统的VAR模型采用信息准则确定最佳滞后阶数的方法，GC-Mixer可以自动检测时间滞后，且尤其适合处理线性数据。

（2）提出了因果推理模型GC-LSTM，它在因果推理部分使用了更加简化的MLP结构，在预测模块使用了LSTM结构，使得模型更注重提取序列间的非线性关系。相比GC-Mixer，在非线性格兰杰因果推理性能和速度均有提升，但没有时滞方面的推理能力。

（3）在线性数据集VAR，非线性数据集Lorenz-96，真实数据集DREAM3，FMRI BOLD上对所提出的模型进行了测试，并且与其他基于深度学习的格兰杰因果模型，如cMLP，cLSTM，GVAR，e-SRU等进行了比较，证明了所提出模型的优越性和有效性。

In the era of big data, the accumulation and analysis of data have become an important means of solving various problems and unlocking value. In many practical scenarios, we are not only interested in the correlation between data but also want to understand the Granger causality between variables. Such causal relationships can help us predict future situations, identify influencing factors, and design effective interventions. Most existing Granger causality inference models assume linear dynamics, yet the vast majority of real-world interactions are nonlinear. In these cases, using linear causal models on nonlinear time series can lead to erroneous Granger causal inference. 

The application of deep learning can well improve the above problem; on the one hand, the nonlinear nature of neural networks enables them to better capture complex causal relationships in multidimensional time series. On the other hand, the time lag of Granger causality can be automatically inferred by combining deep learning with the Lasso penalty, without the need to manually select the lag as in the case of linear models, which further improves the causal inference ability. Therefore, this paper proposes two deep learning-based Granger causal inference models, GC-Mixer and GC-LSTM, by combining deep learning and Lasso penalty, to realize the extraction of Granger causality and automatic inference of time lag from multi-dimensional time series, and the main research and work are as follows: 

(1) The causal inference model GC-Mixer was proposed, which uses multiple stacked MLP mixing blocks to extract the temporal and spatial features of the series respectively and infer the causal relationships among the multidimensional time series. Compared to the traditional VAR model that uses an information criterion to determine the optimal lag order, GC-Mixer can automatically detect time lags and is particularly suitable for dealing with linear data.

(2) The causal inference model GC-LSTM was proposed, which uses a more simplified MLP structure in the causal inference part and an LSTM structure in the prediction module, making the model more focused on extracting nonlinear relationships between sequences. Compared to GC-Mixer, it has improved performance and speed in nonlinear Granger causal inference but does not have the inference ability in terms of time lag.

(3)The proposed model was tested on linear datasets VAR, nonlinear datasets Lorenz-96, real datasets Dream-3, and FMRI BOLD, and compared with other deep learning-based Granger causality models such as cMLP, cLSTM, GVAR, e-SRU, etc., demonstrating the superiority and effectiveness of the proposed model.