Abstract:
This paper presents a novel application of a least squares Finite Element (FE) interpolation procedure for solving "model-free" problems, a class of problems typically addressed by machine learning and deep learning methods. The study's focus is on the problem of recognizing handwritten numbers using the MNIST dataset, which consists of 50,000 greyscale images. Unlike traditional methods, which are global and computationally intensive, the proposed FE interpolation approach is local and requires minimal computing resources. The authors used a full quadratic Lagrange polynomial function to create a finite element grid and successfully interpolated the MNIST data without failures. This method's performance is compared to a deep learning solution, highlighting the computational efficiency and local nature of the FE approach. The results demonstrate the potential of FE interpolation as a viable and resource-light alternative for certain types of image recognition and data-fitting problems.
