Explaining Process Control Optimisation Recommendations via GradientSHAP and Implicit Differentiation

Industrial processes often rely on automated optimization algorithms to adjust control parameters, yet operators frequently distrust these "black-box" recommendations. The authors aim to bridge this trust gap by providing interpretable, natural language explanations for why an optimizer suggests specific changes to operational settings, such as pressure and speed in High Pressure Grinding Roll (HPGR) equipment.

To generate explanations, the researchers combine three techniques:

1. Implicit Differentiation: They use the Implicit Function Theorem (IFT) to calculate the exact sensitivity of optimal parameters with respect to input features. This avoids the need for computationally expensive sampling.
2. GradientSHAP: By leveraging these exact sensitivities, they apply GradientSHAP to attribute changes in the optimizer's output to specific input features. This provides a mathematically grounded way to determine which factors (e.g., feed particle size or production targets) drove a specific recommendation.
3. LLM Narrative Generation: They feed these numerical attributions into a Large Language Model (LLM) to translate technical SHAP values into clear, actionable, and operator-friendly narratives.

In an industrial HPGR case study, the proposed method achieved a correlation of over 0.99 with traditional KernelSHAP (the gold standard for attribution) while delivering a 40-fold increase in computational speed. This efficiency allows for real-time generation of explanations. Feedback from domain experts indicated that the generated narratives were helpful, provided they followed specific design principles: leading with an actionable summary, using intuitive units (e.g., percentages), and omitting raw technical attribution scores that practitioners found confusing.

This work demonstrates that optimization algorithms do not need to be treated as opaque black boxes. By exploiting the mathematical structure of the optimization problem itself, engineers can provide operators with transparent, context-aware justifications for automated decisions. This transparency is critical for ensuring safety and operational efficiency in high-stakes industrial environments.