A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parameters' components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such as classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring its feasibility.

Semantic and Relational Spaces in Science of Science: Deep Learning Models for Article Vectorisation

Over the last century, we observe a steady and exponentially growth of scientific publications globally. The overwhelming amount of available literature makes a holistic analysis of the research within a field and between fields based on manual inspection impossible. Automatic techniques to support the process of literature review are required to find the epistemic and social patterns that are embedded in scientific publications. In computer sciences, new tools have been developed to deal with large volumes of data. In particular, deep learning techniques open the possibility of automated end-to-end models to project observations to a new, low-dimensional space where the most relevant information of each observation is highlighted. Using deep learning to build new representations of scientific publications is a growing but still emerging field of research. The aim of this paper is to discuss the potential and limits of deep learning for gathering insights about scientific research articles. We focus on document-level embeddings based on the semantic and relational aspects of articles, using Natural Language Processing (NLP) and Graph Neural Networks (GNNs). We explore the different outcomes generated by those techniques. Our results show that using NLP we can encode a semantic space of articles, while with GNN we are able to build a relational space where the social practices of a research community are also encoded.