Sequential bi-level regularized inversion with application to hidden reaction law discovery
<|reference_start|>Sequential bi-level regularized inversion with application to hidden reaction law discovery: In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear partial differential equations (PDEs). In [43], the author suggested a bi-level regularization framework. This study significantly improves upon the bi-level algorithm by sequential initialization, yielding accelerated convergence and demonstrable multi-scale effect, while retaining regularizing effect with respect to noise and allows for the usage of inexact PDE solvers. The sequential bi-level approach illustrates its universality through several reaction-diffusion applications, in which the nonlinear reaction law needs to be determined. To demonstrate the applicability of our algorithms, we moreover prove that the proposed tangential cone condition is satisfied.<|reference_end|>
@article{nguyen2024sequential,
    title={Sequential bi-level regularized inversion with application to hidden
  reaction law discovery},
    author={Tram Thi Ngoc Nguyen},
    journal={arXiv preprint arXiv:2409.03834},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03834},
    primaryClass={math.NA cs.NA math.AP math.OC}
}