Accelerating Inverse Problem Solutions with Generative Adversarial Networks

Abstract

nverse problems represent a class of computational challenges where the goal is to estimate unknown system parameters from observed data, with applications ranging from medical imaging to geophysical exploration. These problems are typically ill-posed and computationally intensive, often requiring sophisticated regularization techniques and iterative optimization methods. This comprehensive review explores the transformative potential of Generative Adversarial Networks (GANs) in accelerating solutions to inverse problems across various scientific domains. We examine how GAN architectures can learn complex prior distributions from data, enable rapid parameter estimation, and produce high-fidelity reconstructions while significantly reducing computational burden compared to traditional methods. The paper covers fundamental theoretical concepts, including conditional GANs, Wasserstein GANs with gradient penalty, and physics-informed adversarial approaches that integrate physical constraints into the learning process. Through detailed case studies in seismic imaging, medical reconstruction, materials science, and physical modeling, we demonstrate how GAN-based approaches achieve substantial acceleration often orders of magnitude faster than conventional techniques while maintaining competitive reconstruction quality. The review also addresses current challenges and limitations, such as training instability, theoretical guarantees, and data requirements, while outlining promising future research directions for further advancing the field of accelerated inverse problem solving.