Related papers: Variational PINNs with tree-based integration and …

We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely…

The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of the fine scales in terms of the coarse scales. In linear…

In this study, we propose a novel approach, termed boundary integrated neural networks (BINNs), for analyzing in-plane crack problems within the framework of linear elastic fracture mechanics. The proposed approach integrates artificial…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the…

Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Recent developments in acoustic signal processing have seen the integration of deep learning methodologies, alongside the continued prominence of classical wave expansion-based approaches, particularly in sound field reconstruction.…

The application of the Physics-Informed Neural Networks (PINNs) to forward and inverse analysis of pile-soil interaction problems is presented. The main challenge encountered in the Artificial Neural Network (ANN) modelling of pile-soil…

We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…

Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN)…

We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space…

Continuous reconstructions of periodic phenomena provide powerful tools to understand, predict and model natural situations and engineering problems. In line with the recent method called Physics-Informed Neural Networks (PINN) where a…

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…

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…

We introduce Nonlinear GENERIC Informed Neural Networks (N-GINNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium…

SGM-PINN is a graph-based importance sampling framework to improve the training efficacy of Physics-Informed Neural Networks (PINNs) on parameterized problems. By applying a graph decomposition scheme to an undirected Probabilistic…