With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches adopt the component-wise architecture, necessitating the construction of a separate model for each time series, which results in substantial computational costs. In addition, imposing the sparsity-inducing penalty on the first-layer weights of the neural network to extract causal relationships weakens the model's ability to capture complex interactions. To address these limitations, we propose Gradient Regularization-based Neural Granger Causality (GRNGC), which requires only one time series prediction model and applies $L_{1}$ regularization to the gradient between model's input and output to infer Granger causality. Moreover, GRNGC is not tied to a specific time series forecasting model and can be implemented with diverse architectures such as KAN, MLP, and LSTM, offering enhanced flexibility. Numerical simulations on DREAM, Lorenz-96, fMRI BOLD, and CausalTime show that GRNGC outperforms existing baselines and significantly reduces computational overhead. Meanwhile, experiments on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets further validate the model's effectiveness in reconstructing gene regulatory networks.

翻译：随着深度学习技术的发展，多种基于神经网络的格兰杰因果模型被提出。尽管这些模型取得了显著进步，但仍存在若干局限。现有方法大多采用分量式架构，即需为每个时间序列构建独立模型，导致计算成本高昂。此外，通过引入稀疏性正则化对神经网络首层权重施加惩罚以提取因果关系，会削弱模型捕捉复杂交互的能力。为解决上述问题，我们提出基于梯度正则化的神经格兰杰因果模型（GRNGC），该模型仅需一个时间序列预测模型，通过对模型输入与输出之间的梯度施加$L_{1}$正则化来推断格兰杰因果关系。进一步地，GRNGC不局限于特定时间序列预测模型，可基于KAN、MLP、LSTM等多样化架构实现，从而增强灵活性。在DREAM、Lorenz-96、fMRI BOLD及CausalTime上的数值仿真表明，GRNGC优于现有基线方法，并显著降低计算开销。同时，在DNA、酵母、HeLa及膀胱尿路上皮癌细胞真实数据集上的实验进一步验证了该模型在基因调控网络重构中的有效性。