The field of inverse problems and geophysics is rapidly advancing with the integration of deep learning and data-driven approaches. Researchers are developing innovative methods to tackle complex problems such as visualizing the Earth's subsurface, estimating heterogeneous elastic properties, and solving ill-posed integral equations. These advancements have the potential to revolutionize various applications including resource exploration, hazard assessment, and geotechnical engineering. Noteworthy papers include one that proposes a synthetic data-generator process to extend surface geological data to a three-dimensional subsurface region, and another that presents a novel robust nonlinear filtering method to mitigate challenges in state estimation. Additionally, a paper on linearly solving robust rotation estimation showcases a voting-based method that exhibits exceptional robustness to noise and outliers. Another significant contribution is the development of a data-driven approach to inverse problems, which utilizes highly over-parameterized models and deep neural networks to derive solutions. Overall, the field is moving towards more efficient, accurate, and robust methods for solving inverse problems, with a strong emphasis on integrating machine learning and data-driven techniques.
Advances in Inverse Problems and Geophysics
Sources
Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data
Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations