Towards Parameter-Dependent Data-Enriched Physics-Informed Machine Learning

Efficient and reliable surrogates of real-world systems are core to the solution of tasks such as uncertainty quantification, sensitivity estimation, risk assessment, system identification, or pervasive interaction. Surrogates learned purely from data frequently violate fundamental principles such as conservation laws. To remedy this, we utilize and exetnd methods in the field of Scientific Machine Learning (SciML). These integrate knowledge about the underlying physics into the learning process to restore physical plausibility. This project targets the transition of learned surrogates from standard academic to real-world problems with experimental data, in particular flow problems. We have identified three important challenges: First, data and physics information from different sources have to be balanced based on their fidelity or importance. Second, complex boundaries require new methodological approaches, as standard penalty terms require fine sampling, leading to vast computational demands. And third, model parameters and system parts have to be learned and calibrated to experimental data.