Using Clifford Neural Operators for learning the horizontal and vertical elastic wavefield displacements.

Tianze Zhang, Kristopher A. Innanen, Daniel O. Trad

Neural operators are extensions of neural networks which in supervised training learn how to map complex relationships, such as classes of PDE. Recent literature reports efforts to develop one type of these, the Fourier Neural Operator (FNO), such that it learns to create relatively general solutions to PDEs such as the Navier-Stokes equation. Clifford algebra is very useful for representing multidimensional data. In this study, we use the Clifford Fourier Neural Operator (CFNO) be trained to learn the elastic wave equation from a synthetic training data set. CFNO attempts to find a manifold for elastic wave propagation.On that manifold, wave fields are represented in lower dimensions than those needed for standard solutions, and the calculations for wave propagation are correspondingly simpler.The CFNO combines a linear Clifford fully connected transform, the Clifford Fourier trans-form, and a non-linear local activation to produce a network with sufficient freedom to map from a general parameterization of a forward wave problem to its solution. Post-training,the CFNO is observed to generate accurate elastic wave fields