PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss

By incorporating the residual of the differential equation into the loss function of a neural network-based surrogate model, PINNs can seamlessly combine measured data with physical constraints given by differential equations. PINNs can also be viewed as a surrogate model for solving differential equations by incorporating additional data or as a data-driven correction (or even discovery) of the underlying physical system. By the end of the year 2022, we had experienced several waves of the COVID-19 pandemic with different variants of the virus prevailing at different time intervals. Various levels of interventions and protective measures were implemented to counteract the uncontrolled spreading of the disease. We focus exemplarily on the time until the fourth wave (i.e., the omicron wave) of the COVID-19 pandemic in Germany that had its peak in February and March 2022. The B.1.617.2 (delta) variant of SARS-CoV-2, which is characterized by a higher contagiosity than the previous B.1.1.7 (alpha), B.1.351