Recent breakthroughs in computing power have made it feasible to use machine learning
and deep learning to advance scientific computing in many fields, including fluid mechanics …

Advancements in computing power have recently made it possible to utilize machine
learning and deep learning to push scientific computing forward in a range of disciplines …

Abstract Deep Operator Network (DeepONet), a recently introduced deep learning operator
network, approximates linear and nonlinear solution operators by taking parametric …

This paper presents a literature review on methods for enabling real-time analysis in digital
twins, which are virtual models of physical systems. The advantages of digital twins are …

Physics‐informed neural networks (PINNs) are a new tool for solving boundary value
problems by defining loss functions of neural networks based on governing equations …

The deep energy method (DEM) has been used to solve the elastic deformation of structures
with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on …

Finite element analysis (FEA), a common approach for simulating stress distribution for a
given geometry, is generally associated with high computational cost, especially when high …

In recent years, physics-informed neural networks (PINN) have been used to solve stiff-
PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D …

Physics-informed neural networks (PINNs) have recently prevailed as differentiable solvers
that unify forward and inverse analysis in the same formulation. However, PINNs have quite …

Physics-informed neural networks (PINNs) are well-regarded for their capabilities in inverse
analysis. However, efficient convergence is hard to achieve due to the necessity of …