Mohammad H. Taufik

Xiao Ma, Mohammad Hasyim Taufik, Tariq Alkhalifah

Velocity model building serves as a crucial component for achieving high precision subsurface imaging. However, conventional velocity model building methods are often computationally expensive and time consuming. In recent years, with the rapid advancement of deep learning, particularly the success of generative models and neural operators, deep learning based approaches that integrate data and their statistics have attracted increasing attention in addressing the limitations of traditional methods. In this study, we propose a novel framework that combines generative models with neural operators to obtain high resolution velocity models efficiently. Within this workflow, the neural operator functions as a forward mapping operator to rapidly generate time lag reverse time migration (RTM) extended images from the true and migration velocity models. In this framework, the neural operator is acting as a surrogate for modeling followed by migration, which uses the true and migration velocities, respectively. The trained neural operator is then employed, through automatic differentiation, to gradually update the migration velocity placed in the true velocity input channel with high resolution components so that the output of the network matches the time lag images of observed data obtained using the migration velocity. By embedding a generative model, trained on a high-resolution velocity model distribution, which corresponds to the true velocity model distribution used to train the neural operator, as a regularizer, the resulting predictions are cleaner with higher resolution information. Both synthetic and field data experiments demonstrate the effectiveness of the proposed generative neural operator based velocity model building approach.

Mohammad H. Taufik, Tariq Alkhalifah

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence and the need to perform additional, potentially expensive, training for different PDE parameters. To solve this limitation, we introduce latentPINN, a framework that utilizes latent representations of the PDE parameters as additional (to the coordinates) inputs into PINNs and allows for training over the distribution of these parameters. Motivated by the recent progress on generative models, we promote the use of latent diffusion models to learn compressed latent representations of the PDE parameters distribution and act as input parameters to NN functional solutions. We use a two-stage training scheme in which the first stage, we learn the latent representations for the distribution of PDE parameters. In the second stage, we train a physics-informed neural network over inputs given by randomly drawn samples from the coordinate space within the solution domain and samples from the learned latent representation of the PDE parameters. We test the approach on a class of level set equations given by the nonlinear Eikonal equation. We specifically share results corresponding to three different sets of Eikonal parameters (velocity models). The proposed method performs well on new phase velocity models without the need for any additional training.