The quantitative prediction of process constraints, such as the threshold of deep-penetration laser welding, is an important part of a fast and reliable development of robust process windows for laser processes, which is an important aspect for small batch-size manufacturing. Physics-informed hybrid models, the combination of physics-based models and machine learning, are a promising approach for this task.


Therefore, this contribution presents the application of such a physics-informed hybrid model for the prediction of the threshold of deep-penetration laser welding. The presented model combines an analytical model with a machine learning model, employing Gaussian processes, where the machine learning model is trained to learn and compensate for the deviations between the analytical model and experimental results.


The prediction accuracy could be increased by applying the physics-informed hybrid model, resulting in a reduction of the mean relative error of about 73 % compared to only using the analytical model. Furthermore, compared to only using a black-box machine learning model, the number of training data required to train the model could be reduced and an increased prediction accury for extrapolation could be observed.


In some cases the results of the model, including the confidence interval, resulted in negative values, which is not consistent with the physical boundary conditions for the threshold of deep-penetration laser welding. By applying additional output constraints to the model, using the method of output warping, the compliance of the model with the physical boundary conditions could be further improved, successfully mitigating this issue.