Environment-invariant causal representation learning for industrial multivariate time series forecasting

Causality in industrial processes provides critical insight into how variables interact within a system, revealing latent physical mechanisms that support reliable prediction and engineering interpretability. However, modern machine learning models for industrial forecasting often exploit spurious correlations and therefore fail to generalize across operating environments with distribution shifts. Existing approaches typically pursue invariant representations by suppressing spurious features, yet their generalization claims often rely on independence or restrictive assumptions about latent variables or environments. We propose Environment-invariant Causal Representation Learning (EiCRL) for industrial multivariate time series forecasting. EiCRL is built on a spatio-temporal iterative causal discovery algorithm (stiCD) that estimates causal graphs over dynamic process variables and static covariates. This learned structure induces a flexible, conditionally factorized prior that better matches spatio-temporal dependencies in industrial processes. Based on the discovered structure, we provide an identifiability analysis showing that the resulting causal representation is identifiable up to standard ambiguities relevant to process modeling, and we derive generalization guarantees under environment shifts under mild conditions. We evaluate EiCRL on three real-world datasets, including electricity, air quality, and oilfield datasets. Across all cases, EiCRL consistently outperforms representative baselines from causal discovery, invariant risk minimization, out-of-distribution generalization, and causal representation learning on multi-horizon forecasting tasks. The results demonstrate that explicitly modeling environment-invariant spatio-temporal causal structure can improve out-of-distribution robustness while preserving physical interpretability, which is essential for dependable decision support in industrial process monitoring, soft sensing, and digital-twin applications. • Proposes an environment-invariant causal framework for industrial time-series forecasting. • Learns invariant spatio-temporal causal representations across environments. • Improves robustness under distribution shifts. • Enhances interpretability via DAG-regularized forecasting. • Validated on oilfield, air-quality, and electricity datasets.