Related papers: Exploring energy minimization to model strain loca…

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…

This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic and random initial functions, and with advective term in one,…

Artificial neural networks (ANNs), which are inspired by the brain, are a central pillar in the ongoing breakthrough in artificial intelligence. In recent years, researchers have examined mechanical implementations of ANNs, denoted as…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

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 the principle of minimum potential energy. In this…

For the 3D localization problem using point spread function (PSF) engineering, we propose a novel enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network (PINN)…

We introduce a de novo elastography method to learn the elasticity of solids from measured strains. The deep neural network in our new method is supervised by the theory of elasticity and does not require labeled data for training. Results…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Simulating discontinuities is a long standing problem especially for shock waves with strong nonlinear feather. Despite being a promising method, the recently developed physics-informed neural network (PINN) is still weak for calculating…

A computationally method on damage detection problems in structures was conducted using neural networks. The problem that is considered in this works consists of estimating the existence, location and extent of stiffness reduction in…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean…

Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…

Techniques for training artificial neural networks (ANNs) and convolutional neural networks (CNNs) using simulated dynamical electron diffraction patterns are described. The premise is based on the following facts. First, given a suitable…

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…

Here I introduce an automatic approach to determine the material flow patterns during deformation process using artificial neural networks (ANN). Since deriving and calibrating complex mathematical models for prediction of power…