Towards Facile Deep Learning Architectures for Chemical Processes: Simultaneous Pseudo-Global Training and Economic Synthesis

Abstract

Chemical process data is usually not directly valorized in pure machine learning predictive models due to limited data availability. This limitation often caused from high sensor costs, data variety, and veracity issues. In response, this study proposes a novel formulation based on mixed-integer linear programming (MILP), called Approximated Deep Learning (ADL), to overcome these limitations and enable accurate modeling under data scarcity. The ADL simultaneously performs input selection, outlier filtering, and training of deep learning architectures within a single-level optimization problem. The method approximates the nonlinear and nonconvex components of traditional deep learning models in the mixed-integer domain through sophisticated reformulations, achieving a pseudo-global solution. A key feature of ADL is the integration of sensor pricing as a regularization mechanism, which promotes cost-efficient soft sensor design without compromising predictive performance. The proposed framework is validated on a publicly available bubble column dataset and benchmarked against four conventional deep learning methods. Results show that ADL achieves superior test accuracy with more than 50% reduction in input space, drastically reducing sensor cost. Furthermore, the optimized architecture is a high-quality initial guess for transfer learning on larger datasets. Overall, the method offers a practical and economically viable solution for data-driven chemical process modeling. © 2025 Institution of Chemical Engineers