Physics-Dominant Machine Learning Framework for Welding Operating-Window Boundary Determination

Reliable determination of welding operating windows is essential for achieving robust weld quality, as feasible
process regions are bounded by multiple physical limits, including undersized weld formation at low heat input
and overheating or expulsion at high heat input. Although machine learning (ML) has been increasingly applied
to welding-process modeling, many existing approaches rely primarily on data-driven formulations that provide
limited physical interpretability and may require substantial retraining when operating conditions change.
This work presents a physics-informed and machine-learning-assisted framework for welding operating-
window determination. Physics-informed (PI) analytical models are first developed from the dominant heat-
generation mechanisms of each process, including energy-per-length scaling for high-frequency induction
welding and Joule-heating-based scaling for resistance spot welding. These models establish physically meaningful
operating-window boundaries and provide a compact description of the dominant process behavior. For
situations exhibiting stochastic transition behavior, the framework is extended to a probabilistic formulation to
enable risk-based boundary definition. Machine learning is then introduced only as a residual-correction tool to
account for secondary effects not captured by the analytical formulation. In contrast to approaches in which
machine learning defines the primary model structure, the present framework preserves a physics-dominant
representation while using data-driven methods only to refine residual errors.
The framework is demonstrated using multiple datasets from induction welding and resistance spot welding.
Results show that the physics-informed models capture the primary operating-window structure with relatively
simple analytical expressions, while residual correction provides additional accuracy improvements, particularly
near process-transition boundaries and under conditions exhibiting increased variability. A separate validation
study further demonstrates that although models calibrated for one application cannot be directly transferred to
a different operating condition with acceptable accuracy, the proposed workflow can be systematically reapplied
to develop accurate models for new situations. The results suggest that combining governing physics, residual
analysis, domain knowledge, and machine learning provides a practical and interpretable approach for
operating-window modeling in intelligent manufacturing systems.