A Gradient-Based Causal Discovery Framework With Applications to Complex Industrial Processes

With the rapid development of deep learning, a wide range of neural network-based causal discovery frameworks have emerged. Although these methods have achieved significant advancements, they still face several limitations when deployed in real-world industrial processes. Many existing models follow the component-wise modeling design, where an individual model must be built for each variable. This leads to significant computational overhead, especially in high-dimensional industrial systems. Moreover, imposing sparsity constraints on the first-layer weights of neural networks to discover causal relationships limits their ability to capture complex and nonlinear interactions among variables. To address these challenges, we propose a novel lightweight causal discovery framework, termed gradient-based causal discovery (GCD). Different from conventional component-wise models, GCD only employs a single multilayer perceptron for time-series prediction and leverages$\ell _{1}$regularization on the neural network’s input–output gradient to infer causal relationships. Numerical simulations on the Lorenz-96 and CausalTime show that GCD consistently achieves the state-of-the-art performance. Moreover, evaluations across four industrial processes, including Tennessee-Eastman, ultra-processed food, debutanizer, and gas turbine power generation, demonstrate that GCD significantly reduces computational overhead while maintaining high causal discovery accuracy, highlighting its applicability to complex industrial processes.