Integrating feature attribution and symbolic regression for automatic model structure identification and strategic sampling

Abstract

In today's competitive and dynamic global markets, rapidly designing processes for formulated products – complex blends such as cosmetics, detergents, or personal care goods – is both essential and challenging. Understanding how processing conditions and chemical composition interact to determine product key performance indicators (KPIs) often remains unclear. In this work, we introduce a novel model-based design of experiments (MbDoE) framework that combines artificial neural network feature attribution with symbolic regression (SR) to uncover interpretable physical relationships. By leveraging feature attribution to guide the search within SR's large combinatorial space, our method efficiently targets structural improvements in candidate models. Additionally, a strategic sampling approach determining the most informative time points to measure KPI determining attributes ensures that each experiment yields maximum information. Applied to a comprehensive in-silico case study, the framework successfully recovered the differential equations for the underlying mechanisms driving the rate of change in the KPIs during the formulated product manufacturing process and reduced the required number of experiments threefold, even with limited data availability. These results highlight the significant potential of artificial neural network guided SR-MbDoE to accelerate process flow diagram development, enhance understanding of complex formulated processes, and improve decision-making in the chemical industry.