Law of conservation-guided neural network with gradient aggregation for improved energy efficiency optimization in industrial processes

• Structure-based tutorial of law of conservation guided neural network is proposed. • Gradient aggregation reveals the subsystem dynamic while promoting model liquidity. • The model is verified by vinyl chloride monomer and detergent powder production. • Proposed system modularization identifies energy efficiency hotspots effectively. • Compared to network modification, proposed model boosts performance by 12.2 %. Energy efficiency in industrial systems remains a critical challenge, with traditional data-driven models often limited by model accuracy and data availability. Incorporation of physical laws governing energy systems can improve performance and physical consistency, but the model often struggles with the calculation of loss and ignores dynamic interplays between sub-systems, which can result in oversimplification and a lack of practical applicability. Therefore, this study investigated a theoretical framework for developing a law of conservation-guided neural network aimed at enhancing energy efficiency prediction in industrial systems. The framework integrates physical principles directly into floating nodes constructed using a long short-term memory architecture to help the model formulate the relationship between process variables, while gradient aggregation increases liquidity and interpretability. Through evaluation of two large-scale case studies—vinyl chloride monomer and detergent powder production—the proposed model produced substantial improvements in prediction accuracy and model reliability, with a test prediction improvement of 12.2 % and 5.87 % over published methods. Compared to network architecture modification approaches, the proposed model provided higher reliability and reproducibility in energy efficiency predictions. Moreover, the model successfully identified energy inefficiencies, resulting in a 4.21 % reduction in energy consumption and a corresponding 377.35 tons of carbon emissions reduction.