A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes

[Submitted on 15 Jul 2025 (v1), last revised 16 Jun 2026 (this version, v3)]

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Abstract: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.

Submission history

From: Meiliang Liu [view email]
[v1] Tue, 15 Jul 2025 10:35:29 UTC (641 KB)
[v2] Sat, 25 Oct 2025 12:46:37 UTC (656 KB)
[v3] Tue, 16 Jun 2026 03:33:30 UTC (647 KB)