We worked on the technical development of PINN methods for seismic wavefield computation. In particular, it has become well known since the original development of PINNs in 2019 that they perform very well on "smooth" problems, where as "rough" problems (those with high spatial frequency content) can pose challenges in training. Seismic wavefields are relatively rough as they contain broadband temporal and spatial frequency content. However, data-driven machine learning methods (the vast majority of AI/ML platforms currently extant) can capture high degrees of spatial complexity, at the cost of requiring training data. We recognized that the complexity of the seismic wavefield is primarily in the direction pointing directly away from a seismic source, but that the azimuthal direction is relatively simple (imagine cutting vertically through the center of an orange to take out a wedge; any one wedge looks quite complicated, but if you were to chose another wedge to cut, the two wedges would look very similar - this is azimuthal symmetry). As such, we can train a data-driven machine learning model on a lower-dimensional problem that is simple but still captures the spatial frequency content, and then use a PINN to then solve the more complicated higher dimensional problem using the data-driven solution as a reference. The result is that the PINN does not need to learn complex spatial patterns itself, but rather warps the underlying complexity from the data driven model, thereby avoiding the issue that PINNs have in learning high frequency content. We have reported these results within leading scientific conferences, including in a talk at the American Geophysical Union Fall Meeting 2023, and a publication is in preparation. Performing this research further inspired 3 scientific publications during the project, 2 of which are published in the diamond open access journal Seismica, and one in Geophysical Journal International as a gold open access paper.
