S065-02
Application of Physics-Informed Neural Networks in Solving Full-Waveform Seismic Forward and Inverse Problems

Wednesday, 16 December 2020: 05:36
Virtual
Majid Rashtbehesht, Brown University, Providence, RI, United States, Guofei Pang, Brown university, Providence, United States and Christian Huber, Brown University, Earth, Environmental, and Planetary Sciences, Providence, RI, United States
Abstract:
Seismic inversions are computationally expensive, especially when full waveform tomography is involved. Here, we demonstrate that physics-informed neural networks (PINNs; Raissi et al., 2017), a novel deep learning technique, can be used efficiently to solve the full-waveform forward and inverse problem in both elastic and acoustic media.

Using a novel training technique, we demonstrate that a deep neural network (DNN) is capable of estimating the solution to the full-waveform wave propagation in space and time in acoustic/elastic heterogeneous media. The weights and biases of this DNN are optimized using the ADAM optimizer, which is a variant of the stochastic gradient descent method. The objective of the training process is to minimize simultaneously various loss terms associated with the governing partial differential equations of the acoustic/elastic wave equations, relevant initial and boundary condition, and proper regularization terms.

The convenient analytic properties of DNNs allow us to exploit the efficient symbolic differentiation of TensorFlow for training purposes. Some of the attractive properties of PINNs are: (1) Unlike the conventional data-intensive training of DNNs, PINNs offer an efficient training scheme that takes advantage of the governing partial differential equations and initial /boundary conditions of the problem, which significantly reduces the need for training data, (2) PINNs are advantageous because they provide a meshless approximation of the solution to the partial differential equations. Physics-Informed Neural Networks offer therefore a promising alternative to model forward and inverse wave propagation problems.

Raissi M, Perdikaris P, Karniadakis GE. 2019 Physics-informed neural network: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707. (doi:10.1016/j.jcp.2018.10.045)

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