Surrogate model–aided digital twins for multi-coupling control process parameter optimization

In industrial control, optimizing parameters involves multiple coupled system attributes and is essential for enhancing production efficiency and quality. Traditional methods often rely on physical models for parameter optimization, which tend to have high costs, safety risks, and significant computational complexity. To address these challenges, we introduce a surrogate model–aided digital twin (SMADT) framework comprising a finite element-based physical model and Transformer-Convolutional Neural Networks (Transformer-CNN) surrogate to accurately approximate the inverse of the physical model. The key innovation lies in the fact that this inverse surrogate enables one-shot optimization, directly outputting optimal control parameters for target conditions and eliminating the need for iterative simulations. Additionally, physical model parameters are identified in time by comparing finite element simulation outputs with real-world data. We implemented SMADT in the reflow soldering process in electronics manufacturing, a representative case of multi-coupled parameter optimization. Experimental results show that our surrogate model achieves high fidelity in learning the two-stage inverse mapping: it achieves a mean relative error (MRE) of 1.10% in predicting the complete temperature curve from process indicators, and an MRE of 0.64% in decoding the control parameters from the curve shape. The integrated pipeline yields an average control parameter MRE of 1.73% using limited data. This surrogate model–driven approach provides an efficient and reliable solution for real-time optimization in multi-coupled industrial control systems.