[S-CG50] Driving Solid Earth Science through Machine Learning

[SCG50-P03] Uncertainty quantification in seismic forward and inversion problems using physics-informed generative adversarial neural networks

*Yi Ding¹, Su Chen¹, Xiaojun Li^1,2, Suyang Wang¹ (1.Beijing University of Technology, 2.Institute of Geophysics, China Earthquake Administration)

Keywords:physics-informed neural networks, physics-informed generative adversarial neural networks, uncertainty quantification, wavefield modeling, seismic inversion

While physics-informed neural networks (PINNs) show great potential for critical scientific problems, classical deep learning models often model in a deterministic manner and do not account for measurement noise related to the data or model-form uncertainty resulting from model inadequacy. Researchers have recently begun exploring uncertainty quantification (UQ) analysis methods for physics-informed deep learning. In this paper, we quantify and propagate uncertainties in forward and inversion problems of systems governed by wave equations using physics-informed generative adversarial neural networks. We employ a latent variable model to construct a probabilistic representation of the system's state and train it on data using an adversarial inference procedure. Simultaneously, we leverage physical laws to guide the learning of the generator and discriminator models, ensuring their predictions adhere to wave propagation principles. In order to perform the seismic inversion problem in the framework, we introduce an inversion neural network that approximates the wave velocity. With the trained probabilistic model and inversion network, uncertainties in forward modeling and inversion problems can be propagated using Monte Carlo sampling. Our approach provides a comprehensive comparison with two other popular methods for estimating uncertainties in the PINNs, namely the MC-Dropout PINNs method and the Bayesian physics-informed neural networks (B-PINNs) method. A simple approach to achieving this uncertainty estimation is to implement MC-Dropout within the PINN framework and its variants to generate the distribution of output predictions. However, the small perturbations introduced by MC-Dropout can easily lead to the neural network becoming physically inconsistent, resulting in erroneous outcomes. In B-PINNs, the confidence of the physical constraints is probabilistically modeled, combined with data uncertainty to form a likelihood function. The non-parametric variational inference algorithm Stein Variational Gradient Descent (SVGD) is adopted to achieve Bayesian learning. By presenting a series of examples that showcase the impact of observations with varying levels of noise on uncertainty estimation, we effectively demonstrate the efficacy of our approach in measuring uncertainty for wavefield modeling and seismic inversion problems.