Data-Driven Approach for Inverse Wave Source Problems
Analysis
This paper addresses the challenging inverse source problem for the wave equation, a crucial area in fields like seismology and medical imaging. The use of a data-driven approach, specifically $L^2$-Tikhonov regularization, is significant because it allows for solving the problem without requiring strong prior knowledge of the source. The analysis of convergence under different noise models and the derivation of error bounds are important contributions, providing a theoretical foundation for the proposed method. The extension to the fully discrete case with finite element discretization and the ability to select the optimal regularization parameter in a data-driven manner are practical advantages.
Key Takeaways
- •Develops a data-driven approach for solving the inverse source problem of the wave equation.
- •Analyzes convergence under different noise models using $L^2$-Tikhonov regularization.
- •Establishes error bounds without requiring classical source conditions.
- •Extends the analysis to the fully discrete case with finite element discretization.
- •Provides a basis for selecting the optimal regularization parameter in a data-driven manner.
“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”