We consider the ill-posed inverse problem of identifying parameters in a time-dependent PDE model, whose nonlinearity is supposed to be unknown. The model nonlinearity is represented via a neural network; suggesting an all-at-once approach, we bypass the need for training data. In the general case, the approximation via a neural network can be realized as a discretization scheme. Therefore, we study discretization of regularization in terms of Tikhonov and Landweber methods for the inverse problem, and prove convergence when the discretization error and noise level tend to zero.

翻译：我们认为,在基于时间的PDE模型中确定参数的错误反向问题,这种模型的无线性应该不为人所知。模型的无线性通过神经网络得到体现;建议一种全天候方法,我们忽略了对培训数据的需求。在一般情况下,通过神经网络的近似化可以作为一种离散计划实现。因此,我们研究在蒂克诺诺夫和Landweber方法方面对反向问题的规范化分解,并在离散错误和噪音水平趋向于零时证明趋同。