Oct 2026· Engineering computations· Vol 42· 0 citations· 54 references
TL;DR
The results demonstrate that MNES accurately reproduces the corresponding finite-element energy solutions and highlight the potential of neural reparameterization as an alternative formulation for solving discretized finite-element variational problems.
Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM). The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework. However, their conventional collocation-based implement...
Pius J. M. Wichmann, Stefan Hildebrand, Sandra Klinge· 0 citations
This work presents a variational, label-free physics-informed graph neural network (PI-GNN) in which the heterogeneity is carried by the discretization rather than by the trial field, a variationally consistent, penalty-free interface representation for parametric surrogates and inverse identification rather than a rep...
A. Yadav, Amiya Prakash Das, R. Annabattula· 0 citations
This study considers a two-dimensional dynamic problem of linear elasticity formulated directly in terms of the stress tensor components. A coupled system of differential equations for two normal stress components and one shear stress component is derived from the equations of motion, kinematic relations, and Hooke’s l...
A. Bobonazarov, A. Khaldjigitov, U. Djumayozov et al.· Computation· 0 citations
A framework that integrates the dynamic stiffness matrix (DSM) with physics-informed neural networks (PINN) that embeds physical constraints within the model and demonstrates robustness, particularly when addressing limited datasets across diverse investigations is introduced.
Yi-Jun An, Zhijiang Chen, Zhi-Qiang Feng et al.· 0 citations
The discovery of constitutive laws from experimentally accessible measurements is a central problem in nonlinear computational mechanics. Many data-driven constitutive identification approaches rely either on paired strain–stress data or on full-field displacement measurements, both of which are difficult to obtain i...
Francesco Regazzoni· Computational Mechanics· 1 citation
The study proposes hybrid methodologies combining FEM’s reliability with PINNs’ flexibility to advance 3D electromagnetic simulations, and proposes hybrid methodologies combining FEM’s reliability with PINNs’ flexibility to advance 3D electromagnetic simulations.
Mohammad M. Fakharian· Compel· 0 citations
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