Conclusion and outlook

This article has presented the fundamental principles of physics-inspired statistical learning. This is a very broad field, characterized by the use of physics concepts in conjunction with data-driven learning methods to address physical problems. These so-called "hybrid" methods are an emerging topic of major interest to many scientific communities. Physics can be incorporated into model learning in several ways: through appropriate selection of training data, in the form of soft constraints in the loss function, as hard constraints in neural network architectures, or in a modular fashion. From a learning perspective, these physical constraints enable the development of more interpretable models that conform to physical laws and remain robust in the presence of noisy data. This typically translates into greater efficiency in data utilization and better extrapolation performance beyond...