Causal discovery in industrial systems via physics-guided variational attention and probabilistic interventions

Industry 4.0 technologies demand robust fault detection and diagnosis systems distinguishing genuine causal relationships from spurious correlations in complex industrial processes. Traditional correlation-based approaches exhibit significant limitations with nonlinear dynamics, temporal dependencies, and uncertain operational conditions. This paper presents a physics-guided variational attention framework for causal discovery, integrating log-normal variational attention mechanisms with probabilistic interventions and domain expertise. The dual-attention architecture utilizes multivariate log-normal distributions to model asymmetric, positive-valued causal strengths, addressing limitations of symmetric Gaussian parameterizations. Physics-informed priors from operator knowledge are incorporated through Gaussian Mixture Models and transformed via moment-matching. Uncertainty quantification employs Monte Carlo sampling and conformal filtering for statistically rigorous causal validation. Evaluation across synthetic time-series data, Australian Refinery Process oscillation diagnosis, and Tennessee Eastman Process demonstrates superior performance versus baseline approaches. Log-normal variational attention consistently outperforms Gaussian alternatives, with physics-informed priors providing improvements under high-uncertainty conditions, establishing a robust foundation for industrial causal discovery applications.