Sequential bi-level regularized inversion with application to hidden reaction law discovery
arXiv:2409.03834 · doi:10.1088/1361-6420/addf73
Abstract
In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In our recent work, we introduced a bi-level regularization framework. This study significantly improves upon the bi-level algorithm by sequentially initializing the lower-level problem, yielding accelerated convergence and demonstrable multi-scale effect, while retaining regularizing effect and allows for the usage of inexact PDE solvers. Moreover, by collecting the lower-level trajectory, we uncover an interesting connection to the incremental load method. The sequential bi-level approach illustrates its universality through several reaction-diffusion applications, in which the nonlinear reaction law needs to be determined. We moreover prove that the proposed tangential cone condition is satisfied.
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