Related papers: Soft Partition-based KAPI-ELM for Multi-Scale PDEs

Introducing a reduced particle stiffness in discrete element method (DEM) allows for bigger time steps and therefore fewer total iterations in a simulation. Although this approach works well for dry non-adhesive particles, it has been shown…

Scientific machine learning (SciML) is increasingly applied to in-field processing, controlling, and monitoring; however, wide-area sensing, real-time demands, and strict energy and reliability constraints make centralized SciML…

Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous…

We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…

Flexoelectricity refers to a phenomenon which involves a coupling of the mechanical strain gradient and electric polarization. In this study, a meshless Fragile Points Method (FPM), is presented for analyzing flexoelectric effects in…

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…

Metal additive manufacturing enables unprecedented design freedom and the production of customized, complex components. However, the rapid melting and solidification dynamics inherent to metal AM processes generate heterogeneous,…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss…

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…

Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like Deep Operator Networks (DeepONets) require extensive labeled…

In this work, we propose a new particle-based variational inference (ParVI) method for accelerating the Energetic Variational Inference with Implicit scheme (EVI-Im) introduced in Ref. \cite{wang2021particle}. Inspired by energy…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…

The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…

We present two efficient numerical methods for susceptibility artifact correction applicable in Echo Planar Imaging (EPI), an ultra fast Magnetic Resonance Imaging (MRI) technique widely used in clinical applications. Both methods address a…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of…

Semiconductor imaging and analysis are critical yet understudied in deep learning, limiting our ability for precise control and optimization in semiconductor manufacturing. We introduce a small-scale multimodal framework for analyzing…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…