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
Synthetic Geology -- Structural Geology Meets Deep Learning
Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
On existence of a variational regularization parameter under Morozov's discrepancy principle
Robust Filtering -- Novel Statistical Learning and Inference Algorithms with Applications
Linearly Solving Robust Rotation Estimation
Harvest and Jam: Optimal Self-Sustainable Jamming Attacks against Remote State Estimation
Data-driven approaches to inverse problems
Observer Switching Strategy for Enhanced State Estimation in CSTR Networks
Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data
Convergence of generalized cross-validation with applications to ill-posed integral equations
Bayesian Knowledge Transfer for a Kalman Fixed-Lag Interval Smoother
Posterior contraction rates of computational methods for Bayesian data assimilation
Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations
Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver
Acoustic Waveform Inversion with Image-to-Image Schr\"odinger Bridges