Rule-Based neural surrogate for real-time FEM prediction in H-Beam manufacturing

This paper presents a surrogate modeling framework for predicting point-level geometric and thermal characteristics, providing a computationally efficient alternative to traditional Finite Element Method (FEM) simulations. To demonstrate the effectiveness of the proposed framework, we adapt three neural network approaches: (1) a conventional residual multilayer perceptron (Residual MLP); (2) a feature-engineered Residual MLP enhanced with geometric domain knowledge, such as distances from points to cast boundaries; and (3) a novel model termed Deep Controllable Rule Learning with Joint Feasibility and Selectivity (DeepCTRL-JFS). DeepCTRL-JFS extends the original DeepCTRL framework by interpreting implicit process rules as joint feasible regions over multiple response variables and softly guiding predictions toward rule-compliant outputs through selective penalty application. Comparative evaluations confirm that explicitly embedding geometric knowledge–either through enriched input features or architectural constraints–leads to substantial improvements in overall model performance. The primary contribution of this study lies in demonstrating that incorporating domain-specific process knowledge into surrogate models, through either feature engineering or rule-based neural network architectures, significantly improves predictive accuracy and generalization capability. As a result, the proposed methodology can accelerate numerical simulations by providing fast and accurate surrogate predictions and can also support manufacturing process optimization by effectively integrating domain-specific knowledge into the learning framework.