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

arXiv: https://arxiv.org/abs/2507.11178 · HTML: https://mlsanity.com/paper/2507.11178/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking Causal Discovery methods](https://mlsanity.com/paper/2208.01529/) (2022)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [Kolmogorov-Arnold Networks for Time Series Granger Causality Inference](https://mlsanity.com/paper/2501.08958/) (2025)
- [A causal model of safety assurance for machine learning](https://mlsanity.com/paper/2201.05451/) (2022)

## Abstract (arXiv)

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 L1 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.