The finite element method (FEM) is a popular tool for solving engineering problems governed by Partial Differential Equations (PDEs). The accuracy of the numerical solution depends on the quality of the computational mesh. We consider the self-adaptive hp-FEM, which generates optimal mesh refinements and delivers exponential convergence of the numerical error with respect to the mesh size. Thus, it enables solving difficult engineering problems with the highest possible numerical accuracy. We replace the computationally expensive kernel of the refinement algorithm with a deep neural network in this work. The network learns how to optimally refine the elements and modify the orders of the polynomials. In this way, the deterministic algorithm is replaced by a neural network that selects similar quality refinements in a fraction of the time needed by the original algorithm.

To face the increasing demand of quality healthcare, cutting-edge automation technology is being applied in demanding areas such as medical imaging. This paper proposes a novel approach to classification problems on datasets with sparse highly localized features. It is based on the use of a saliency map in the amplification of features. Unlike previous efforts, this approach does not use any prior information about feature localization. We present an experimental study based on the Diabetic Retinopathy classification problem, in which our method has shown to achieve an over 20%-higher accuracy in solving a twoclass Diabetic Retinopathy classification problem than a naive approach based solely on residual neural networks. The dataset consists of 35,120 images of various qualities, inconsistent resolutions, and aspect ratios.

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