TerraPINN: solving the seismic wave equation with physics informed neural networks

Jack B. Muir, & Tarje Nissen-Meyer

Published September 11, 2022, SCEC Contribution #11971, 2022 SCEC Annual Meeting Poster #115 (PDF)

Deep neural networks have revolutionised our ability to process and classify big data. In seismology in particular, neural network solutions now outperform human analysts in accuracy on standard observational tasks, while allowing orders of magnitude more data to be processed. This revolution was only possible, however, because of the large, high quality labeled datasets accrued by researchers over many decades. As we move towards the next generation of geophysical machine learning, we are beginning to tackle problems where such labelled data is not available. One of the most pressing challenges is the solution of the forward seismic wave equation using deep learning. Ideally, by significantly accelerating existing solvers, we would be able to generate much larger ensembles of seismic wavefield data through realistic media. However, because the forward solution is intrinsically expensive, we do not have large volumes of training data. The physics informed neural network (PINN) framework offers a way to circumvent this problem. Instead of training on synthetic data, we propose solutions and then penalise their misfit to the wave equation. Early investigations of PINNs have shown much promise, however they have so far struggled to solve multi scale problems, such as the seismic wave equation. In TerraPINN, we propose a hybrid approach between PINNs and traditional supervised machine learning. Recognising the approximate axisymmetry of seismic wave propagation, we first fit a reduced dimension radial wavefield in a laterally homogeneous and isotopic medium using a traditional supervised machine learning framework. We then expand azimuthally and train for a correction operator using PINNs. The combined network size has 2 orders of magnitude fewer parameters and trains 10x faster than an equivalent naive PINN formulation in 2D acoustic test cases.

Citation
Muir, J. B., & Nissen-Meyer, T. (2022, 09). TerraPINN: solving the seismic wave equation with physics informed neural networks. Poster Presentation at 2022 SCEC Annual Meeting.

Related Projects & Working Groups
Computational Science (CS)