| Abstract: |
| This talk addresses the robustness of the Adaptive Eigenspace Inversion (AEI) method for inverse problems arising in partial differential equations. Such problems frequently involve the reconstruction of unknown parameters from noisy measurements, where stability and reliability are critical challenges.
A revised framework is proposed by re-examining two key regularisation mechanisms. The number of eigenfunctions is selected using a sensitivity-based criterion, ensuring that only the most influential modes contribute to the reconstruction process. In parallel, the diffusivity cancellation parameter is analysed and shown to play a central role in stabilising the method, leading to the identification of an effective choice.
Morozov`s discrepancy principle is further incorporated to guide the adaptation process in the presence of data uncertainty. The resulting approach, termed adaptive-$\varepsilon$ ASI, demonstrates improved stability and efficiency. Numerical experiments highlight its advantages over the original AEI method and standard techniques such as Tikhonov regularisation. |
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