Locking-free energy-based physics-informed neural networks for shear-deformable beams and plates

Physics-informed neural networks (PINNs) embed governing equations into the training objective and provide a data-efficient machine-learning framework for problems governed by partial differential equations (PDEs). When applying the PINN framework to stiff PDEs, a deterioration of training speed and accuracy can be observed. From a mathematical perspective, the high ratio of coefficients in a stiff PDE is the source of locking effects, known from other discretization schemes. This work investigates transverse shear locking in PINNs for Timoshenko beams and Reissner–Mindlin plates and proposes effective mitigation strategies. We implement energy-based PINNs using different parametrizations of the kinematics: the standard parametrization and hierarchic parametrizations. Our results demonstrate that standard approaches exhibit severe locking behavior, with training speed deteriorating significantly as the slenderness increases. Based on an in-depth study of the training dynamics, we identify the causes of transverse shear locking in PINNs considered in this work. To address them, we adapt hierarchic formulations from structural mechanics to the PINN framework by: (1) using hierarchic formulations that directly parametrize the shear deformation, (2) employing separate neural networks for each primary variable to isolate the trainable parameters, and (3) introducing a slenderness-dependent scaling factor for the shear deformation variable to balance the gradients of the energy terms for training. The proposed method achieves fast, slenderness-independent training and convergence for both beam and plate problems for all variables of interest. The method is developed using energy-based forward-solving PINNs, and its transfer to related PDE-loss-based learning frameworks is illustrated with a parametric PINN.

Subjects

Beams

Hierarchic formulations

Physics-informed neural networks

Plates

Shear locking

Structural mechanics

DDC Class

531: Classical Mechanics

620.1: Engineering Mechanics and Materials Science

Lizenz

https://creativecommons.org/licenses/by/4.0/

Publication version

publishedVersion

Name

1-s2.0-S0045782526005682-main.pdf

Type

Main Article

Size

8.66 MB

Format

Adobe PDF

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Locking-free energy-based physics-informed neural networks for shear-deformable beams and plates