Physics informed machine learning: Seismic wave equation
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Abstract
Similar to many fields of sciences, recent deep learning advances have been applied extensively in geosciences for
both small- and large-scale problems. However, the necessity of using large training data and the ‘black box’
nature of learning have limited them in practice and difficult to interpret. Furthermore, including the governing
equations and physical facts in such methods is also another challenge, which entails either ignoring the physics
or simplifying them using unrealistic data. To address such issues, physics informed machine learning methods
have been developed which can integrate the governing physics law into the learning process. In this work, a 1-
dimensional (1D) time-dependent seismic wave equation is considered and solved using two methods, namely
Gaussian process (GP) and physics informed neural networks. We show that these meshless methods are trained
by smaller amount of data and can predict the solution of the equation with even high accuracy. They are also
capable of inverting any parameter involved in the governing equation such as wave velocity in our case. Results
show that the GP can predict the solution of the seismic wave equation with a lower level of error, while our
developed neural network is more accurate for velocity (P- and S-wave) and density inversion.
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