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The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

Deep neural networks (DNNs) are known to perform well when deployed to test distributions that shares high similarity with the training distribution. Feeding DNNs with new data sequentially that were unseen in the training distribution has…

Generalized eigenvalue proximal support vector machine (GEPSVM) has attracted widespread attention due to its simple architecture, rapid execution, and commendable performance. GEPSVM gives equal significance to all samples, thereby…

It has been observed that deep neural networks (DNNs) often use both genuine as well as spurious features. In this work, we propose "Amending Inherent Interpretability via Self-Supervised Masking" (AIM), a simple yet interestingly effective…

Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as finite element methods, with solutions over the…

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the…

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…

As algorithmic decision-making systems are becoming more pervasive, it is crucial to ensure such systems do not become mechanisms of unfair discrimination on the basis of gender, race, ethnicity, religion, etc. Moreover, due to the inherent…

A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approach exploits the local kernel theory which allows one to…

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation…

Machine learning is used to make decisions for individuals in various fields, which require us to achieve good prediction accuracy while ensuring fairness with respect to sensitive features (e.g., race and gender). This problem, however,…

An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…

In this work, we analyze a penalized variant of the {\phi}-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The {\phi}-FEM is a recently introduced unfitted finite element method based on a level-set description of…

Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…

Scalable and generalizable physics-aware deep learning has long been considered a significant challenge with various applications across diverse domains ranging from robotics to molecular dynamics. Central to almost all physical systems are…

The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the…

Achieving carbon neutrality within industrial operations has become increasingly imperative for sustainable development. It is both a significant challenge and a key opportunity for operational optimization in industry 4.0. In recent years,…