Related papers: A deep learning energy method for hyperelasticity …

Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…

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…

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 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,…

Self-sensing conductive composites can reveal deformation and damage through measurable changes in electrical resistance, which makes them attractive for embedded diagnostics and learning-enabled structural health monitoring. This paper…

Physics-informed neural networks (PINNs) in energy form, also known as the deep energy method (DEM), offer advantages over strong-form PINNs such as lower-order derivatives and fewer hyperparameters, yet dedicated and user-friendly software…

Dual-energy computed tomography (DECT) enables material-specific imaging through acquisitions at two different X-ray energy spectra. Material decomposition from DECT data is an ill-posed inverse problem that is highly sensitive to noise…

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the…

Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data…

In recent years, the rapid advancement of deep learning has significantly impacted various fields, particularly in solving partial differential equations (PDEs) in the realm of solid mechanics, benefiting greatly from the remarkable…

The introduction of Physics-informed Neural Networks (PINNs) has led to an increased interest in deep neural networks as universal approximators of PDEs in the solid mechanics community. Recently, the Deep Energy Method (DEM) has been…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a…

In practical structural design and solid mechanics simulations, material properties inherently exhibit random variations within bounded intervals. However, evaluating mechanical responses under continuous material uncertainty remains a…

This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…

We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…

Physics-Informed Neural Networks (PINNs) have recently emerged as powerful tools for solving partial differential equations (PDEs), with the Deep Energy Method (DEM) proving especially effective in fracture mechanics due to its energy-based…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Physics-Informed Neural Networks (PINNs) have gained considerable interest in diverse engineering domains thanks to their capacity to integrate physical laws into deep learning models. Recently, geometry-aware PINN-based approaches that…

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…