Theory-inspired machine learning—towards a synergy between knowledge and data

Most engineering domains abound with models derived from first principles that have beenproven to be effective for decades. These models are not only a valuable source of knowledge, but they also form the basis of simulations. The recent trend of digitization has complemented these models with data in all forms and variants, such as process monitoring time series, measured material characteristics, and stored production parameters. Theory-inspired machine learning combines the available models and data, reaping the benefits of established knowledge and the capabilities of modern, data-driven approaches. Compared to purely physics- or purely data-driven models, the models resulting from theory-inspired machine learning are often more accurate and less complex, extrapolate better, or allow faster model training or inference. In this short survey, we introduce and discuss several prominent approaches to theory-inspired machine learning and show how they were applied in the fields of welding, joining, additive manufacturing, and metal forming.