Pdarts: Projected Differentiable Architecture Search for Seismic Inversion

Abstract

Seismic inversion is an inverse problem that minimizes both amplitude and phase differences between simulated signals and real observed signals through an optimization problem. Due to its high computational cost and the industry demand for higher resolution, researchers often explore ways to accelerate the process and improve its accuracy. In the last decade, deep learning emerged as a promising alternative for seismic inversion; however, it still requires laborious trial and error processes, integration of domain knowledge, and hyperparameter tuning. To improve the model architectures for this task, this article introduces PDARTS (Projected Differentiable Architecture Search), a method inspired by DARTS and originally designed for seismic inversion. PDARTS enables the use of Fourier and U-Fourier neural blocks, which are expected to generalize well in this context, as they naturally encode long-range spatial correlations and operate in the frequency domain, better capturing the physics properties of seismic data. Since the 2D Fast Fourier Transforms used in this article require square inputs for efficient computation, the asymmetric shape of the original seismic data requires the enforcement of a square input format to ensure proper operation. To achieve this, PDARTS employs fixed encoder layers connected to a projection layer to reshape spatial dimensions and a convolutional layer to mitigate potential artifacts introduced by this reshaping. The decoder, along with the final layers of the encoder, is implemented as a DARTS supernetwork, where neural architecture search (NAS) is conducted to explore the potential of Fourier and U Fourier neural blocks, with the aim of discovering new neural networks with better performance. Experiments demonstrated that the best architecture discovered by our method, PDARTSNet, outperforms current state-of-the-art neural networks for seismic inversion. Furthermore, it demonstrates that despite the increased number of network parameters and consequent higher computational costs, PDARTS has proven capable of discovering neural networks with superior performance for seismic inversion.