Overview of Physics-Informed Machine Learning Inversion of Geophysical Data

no code implementations • 12 Oct 2023 • Gerard T. Schuster, Shihang Feng

The unifying equation is given by the joint objective function $\epsilon$: \begin{eqnarray} \epsilon^{||-PIML}&=&\lambda_1 \overbrace{||{\bf W}^{ML}({\bf H}_{{\bf w}} {\bf d}^{obs}-{\bf m})||^2}^{NN} + \lambda_2 \overbrace{{||{\bf W}^{FWI}({\bf L} {\bf m}-{\bf d}^{obs})||^2}}^{FWI} ~+ \nonumber\\ \nonumber\\ && + ~~Regularizer, \label{PIML. eq120} \end{eqnarray}where the optimal model ${\bf m}^*$ and weights $\bf w^*$ minimize $\epsilon$.

Physics-informed machine learning