Enhanced physics‐informed neural networks for hyperelasticity

Abueidda, Diab W.; Korić, Seid; Guleryuz, Erman; Sobh, Nahil

doi:10.1002/nme.7176

Cited by 37 publications

(11 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Discussionmentioning

confidence: 99%

“…Physics-informed neural networks (PINNs) [52], which attracted a lot of attentions in the field of scientific machine learning, offers a direct solution to PDEs by using DNNs and physics principles. Although PINNs are intriguing, current PINNs have not led to performance improvement compared with commercial FEA methods in the solid mechanics domain and suffer from the error/instability [53] in the deformation gradient tensor calculated by differentiating a DNN with respect to the input: where h ( X ) is a DNN to output displacement. The instability is not a numerical defect of autograd, and it is closely related to the well-known issue of DNN robustness [54], and it is known that [55, 56] gradients of a DNN can change dramatically if the input changes only a little or even if the same DNN is trained twice on the same data.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Liang

Liu

Elefteriades

et al. 2023

Preprint

View full text Add to dashboard Cite

Motivation: Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed. Methods: In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance. Results: We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Liang

Liu

Elefteriades

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The modification allowed the successful resolution of stresses around the stress concentration regions. Abueidda et al 44 enhanced the model by developing PINN that combines residuals of the strong form and the system's potential energy. The proposed formulation yielded a loss function with multiple loss terms.…”

Section: Introductionmentioning

confidence: 99%

Improving the Accuracy of the Deep Energy Method

Chadha¹,

He²,

Abueidda³

et al. 2023

Preprint

View full text Add to dashboard Cite

The deep energy method (DEM), a type of physics-informed neural network, is evolving as an alternative to finite element analysis. This method employs the principle of minimum potential energy to predict deformations under static loading conditions. However, the model’s accuracy is contingent upon choosing the appropriate architecture for the model, which can be challenging due to the high interactions between hyperparameters, large search space, difficulty in identifying objective functions, and non-convex relationships with the objective functions. To improve DEM’s accuracy, we first introduce random Fourier feature (RFF) mapping. RFF mapping helps with the training of the model by reducing bias towards high frequencies. The effects of six hyperparameters are then studied under compression, tension, and bending loads in planar linear elasticity. Based on this study, a systematic automated hyperparameter optimization approach is proposed. Due to the high interaction between hyperparameters and the non-convex nature of the optimization problem, Bayesian optimization algorithms are used. The models trained using optimized hyperparameters and having Fourier feature mapping can accurately predict deflections compared to finite element analysis. Additionally, the deflections obtained for tension and compression load cases are more sensitive to variations in hyperparameters than bending.

show abstract

“…29 The idea is also further extended to a so-called mixed formulation, where both strong form and weak form are utilized simultaneously. 7,22,30,31 One important aspect of engineering applications is to consider the multi-physical characteristics. In other words, in many realistic problems, various coupled and highly nonlinear fields have to be considered simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Mixed formulation of physics‐informed neural networks for thermo‐mechanically coupled systems and heterogeneous domains

Harandi,

Moeineddin,

Kaliske

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

Physics‐informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have shown that when designing loss functions for many engineering problems, using first‐order derivatives and combining equations from both strong and weak forms can lead to much better accuracy, especially when there are heterogeneity and variable jumps in the domain. This new approach is called the mixed formulation for PINNs, which takes ideas from the mixed finite element method. In this method, the PDE is reformulated as a system of equations where the primary unknowns are the fluxes or gradients of the solution, and the secondary unknowns are the solution itself. In this work, we propose applying the mixed formulation to solve multi‐physical problems, specifically a stationary thermo‐mechanically coupled system of equations. Additionally, we discuss both sequential and fully coupled unsupervised training and compare their accuracy and computational cost. To improve the accuracy of the network, we incorporate hard boundary constraints to ensure valid predictions. We then investigate how different optimizers and architectures affect accuracy and efficiency. Finally, we introduce a simple approach for parametric learning that is similar to transfer learning. This approach combines data and physics to address the limitations of PINNs regarding computational cost and improves the network's ability to predict the response of the system for unseen cases. The outcomes of this work will be useful for many other engineering applications where deep learning is employed on multiple coupled systems of equations for fast and reliable computations.

show abstract

Enhanced physics‐informed neural networks for hyperelasticity

Cited by 37 publications

References 44 publications

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Improving the Accuracy of the Deep Energy Method

Mixed formulation of physics‐informed neural networks for thermo‐mechanically coupled systems and heterogeneous domains

Contact Info

Product

Resources

About