Fast numerical solvers for parameter identification problems in mathematical biology
<|reference_start|>Fast numerical solvers for parameter identification problems in mathematical biology: In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization of the optimization problem, we devise appropriate time-stepping schemes and discrete approximations of the cost functionals such that the discretization and optimization operations are commutative, a highly desirable property of a discretization of such problems. We formulate the large-scale, coupled linear systems in such a way that efficient preconditioned iterative methods can be applied within a Krylov subspace solver. Numerical experiments demonstrate the viability and efficiency of our approach.<|reference_end|>
@article{benková2024fast,
    title={Fast numerical solvers for parameter identification problems in
  mathematical biology},
    author={Karol'ina Benkov'a, John W. Pearson, Mariya Ptashnyk},
    journal={arXiv preprint arXiv:2408.14926},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14926},
    primaryClass={math.NA cs.NA math.OC}
}