Gräser, C. and Alathur Srinivasan, P. A. (2020) Error bounds for PDEregularized learning. arXiv:2003.06524 . pp. 120. (Submitted)

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Official URL: https://arxiv.org/abs/2003.06524
Abstract
In this work we consider the regularization of a supervised learning problem by partial differential equations (PDEs) and derive error bounds for the obtained approximation in terms of a PDE error term and a data error term. Assuming that the target function satisfies an unknown PDE, the PDE error term quantifies how well this PDE is approximated by the auxiliary PDE used for regularization. It is shown that this error term decreases if more data is provided. The data error term quantifies the accuracy of the given data. Furthermore, the PDEregularized learning problem is discretized by generalized Galerkin discretizations solving the associated minimization problem in subsets of the infinite dimensional functions space, which are not necessarily subspaces. For such discretizations an error bound in terms of the PDE error, the data error, and a best approximation error is derived.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2421 
Deposited By:  Ekaterina Engel 
Deposited On:  23 Mar 2020 09:27 
Last Modified:  23 Mar 2020 09:27 
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