# A data-driven model reduction method for parabolic inverse source problems and its convergence analysis

@article{Wang2021ADM, title={A data-driven model reduction method for parabolic inverse source problems and its convergence analysis}, author={Zhongjian Wang and Wenlong Zhang and Zhiwen Zhang}, journal={ArXiv}, year={2021}, volume={abs/2110.07676} }

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the solution space of the parabolic partial differential equations (PDEs) in the forward problem with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension…

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