arXiv subjects

Georgios Is. Detorakis

Publications and source records attributed to Georgios Is. Detorakis.

3 recordsLinked to original sources

arXiv2026

Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer

Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this article to introduce students to Deep Galerkin method and scientific deep learning. We focus on key questions: What is deep learning, and how can it help solve mathematical or physical problems? How can you implement a neural network and choose the right numerical method to solve differential equations? How do you select the best hyperparameters? How can you improve accuracy and speed up convergence? We should mention that all the problems in this article can be solved on a machine without a GPU, so any student can follow the presented methodology.

cs.LG↗

arXiv2020

Randomized Self Organizing Map

We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies possess random (but controllable) discontinuities that allow for a more flexible self-organization, especially with high-dimensional data. The proposed algorithm is tested on one-, two- and three-dimensions tasks as well as on the MNIST handwritten digits dataset and validated using spectral analysis and topological data analysis tools. We also demonstrate the ability of the randomized self-organizing map to gracefully reorganize itself in case of neural lesion and/or neurogenesis.

cs.NE↗

arXiv2014

SPySort: Neuronal Spike Sorting with Python

Extracellular recordings with multi-electrode arrays is one of the basic tools of contemporary neuroscience. These recordings are mostly used to monitor the activities, understood as sequences of emitted action potentials, of many individual neurons. But the raw data produced by extracellular recordings are most commonly a mixture of activities from several neurons. In order to get the activities of the individual contributing neurons, a pre-processing step called spike sorting is required. We present here a pure Python implementation of a well tested spike sorting procedure. The latter was designed in a modular way in order to favour a smooth transition from an interactive sorting, for instance with IPython, to an automatic one. Surprisingly enough - or sadly enough, depending on one's view point -, recoding our now 15 years old procedure into Python was the occasion of major methodological improvements.

cs.CE↗