FEA-Net: A physics-guided data-driven model for efficient mechanical response prediction

Yao, Houpu; Gao, Yi; Liu, Yongming

doi:10.1016/j.cma.2020.112892

Cited by 64 publications

(21 citation statements)

References 40 publications

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“…As the learning task of interest is not directly related to the inputs to the model with a hard theory-respecting regularization function like those in [38]- [41] due to the inherent complexity of sheet metal bending engineering problems, a more tricky process of hyperparameters tuning than those for PINN could potentially be needed. As a consequence, the method would increase the computational cost compared to the PINN with PDE governing equations.…”

Section: Learning With Scarce Training Datamentioning

confidence: 99%

“…In this method, one or several governing equations in the research area, normally nonlinear partial differential equations (PDE), are used and converted to one or several physics-informed regularization term in the objective function. In [38]- [41], PINNs were used to predict numerical solutions of governing equations in computational fluid dynamics (CFD). It was reported to outperform pure-data driven DNNs with less training data.…”

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confidence: 99%

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Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network

Liu

Xia

Shi

et al. 2021

IEEE/CAA J. Autom. Sinica

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Sheet metal forming technologies have been intensively studied for decades to meet the increasing demand for lightweight metal components. To surmount the springback occurring in sheet metal forming processes, numerous studies have been performed to develop compensation methods. However, for most existing methods, the development cycle is still considerably time-consumptive and demands high computational or capital cost. In this paper, a novel theory-guided regularization method for training of deep neural networks (DNNs), implanted in a learning system, is introduced to learn the intrinsic relationship between the workpiece shape after springback and the required process parameter, e.g., loading stroke, in sheet metal bending processes. By directly bridging the workpiece shape to the process parameter, issues concerning springback in the process design would be circumvented. The novel regularization method utilizes the well-recognized theories in material mechanics, Swift's law, by penalizing divergence from this law throughout the network training process. The regularization is implemented by a multi-task learning network architecture, with the learning of extra tasks regularized during training. The stress-strain curve describing the material properties and the prior knowledge used to guide learning are stored in the database and the knowledge base, respectively. One can obtain the predicted loading stroke for a new workpiece shape by importing the target geometry through the user interface. In this research, the neural models were found to outperform a traditional machine learning model, support vector regression model, in experiments with different amount of training data. Through a series of studies with varying conditions of training data structure and amount, workpiece material and applied bending processes, the theory-guided DNN has been shown to achieve superior generalization and learning consistency than the data-driven DNNs, especially when only scarce and scattered experiment data are available for training which is often the case in practice. The theory-guided DNN could also be applicable to other sheet metal forming processes. It provides an alternative method for compensating springback with significantly shorter development cycle and less capital cost and computational requirement than traditional compensation methods in sheet metal forming industry.

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Section: Learning With Scarce Training Datamentioning

confidence: 99%

mentioning

confidence: 99%

Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network

Liu

Xia

Shi

et al. 2021

IEEE/CAA J. Autom. Sinica

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“…Using the FEM to inspire a novel neural network architecture, Koeppe et al (2020a) developed a deep convolutional recurrent neural network architecture that maps Dirichlet boundary constraints to force response and discretized field quantities in intelligent meta elements. Yao et al (2020) used physicsinformed deep convolutional neural networks to predict mechanical responses. Thus, using physics-informed approaches, neural networks with more parameters became feasible, whose architecture could be designed and explained using prior mechanical knowledge.…”

Section: Introductionmentioning

confidence: 99%

Explainable Artificial Intelligence for Mechanics: Physics-Explaining Neural Networks for Constitutive Models

et al. 2022

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(Artificial) neural networks have become increasingly popular in mechanics and materials sciences to accelerate computations with model order reduction techniques and as universal models for a wide variety of materials. However, the major disadvantage of neural networks remains: their numerous parameters are challenging to interpret and explain. Thus, neural networks are often labeled as black boxes, and their results often elude human interpretation. The new and active field of physics-informed neural networks attempts to mitigate this disadvantage by designing deep neural networks on the basis of mechanical knowledge. By using this a priori knowledge, deeper and more complex neural networks became feasible, since the mechanical assumptions can be explained. However, the internal reasoning and explanation of neural network parameters remain mysterious. Complementary to the physics-informed approach, we propose a first step towards a physics-explaining approach, which interprets neural networks trained on mechanical data a posteriori. This proof-of-concept explainable artificial intelligence approach aims at elucidating the black box of neural networks and their high-dimensional representations. Therein, the principal component analysis decorrelates the distributed representations in cell states of RNNs and allows the comparison to known and fundamental functions. The novel approach is supported by a systematic hyperparameter search strategy that identifies the best neural network architectures and training parameters. The findings of three case studies on fundamental constitutive models (hyperelasticity, elastoplasticity, and viscoelasticity) imply that the proposed strategy can help identify numerical and analytical closed-form solutions to characterize new materials.

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“…In physics simulation field, the CNN have been applied in discoverying underlying PDEs discovery (Long et al (2018); Long et al (2019)), PDEs solving (Yao et al (2020); Zhu et al (2019)), and surrogate model construction (Zhu et al (2019)). Yao et al (2020) presented that finite element method (FEA) models for PDEs is a special CNN, and FEA-Net was developed to predict the response of materials and structures. Kim et al (2019) effect of different network components is thoroughly discussed, which is helpful for researches of network structure design in this field.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data

Wang¹,

Gong²,

Zhang³

et al. 2021

Preprint

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Recently, surrogate models based on deep learning have attracted much attention for engineering analysis and optimization. As the construction of data pairs in most engineering problems is timeconsuming, data acquisition is becoming the predictive capability bottleneck of most deep surrogate models, which also exists in surrogate for thermal analysis and design. To address this issue, this paper develops a physics-informed convolutional neural network (CNN) for the thermal simulation surrogate. The network can learn a mapping from heat source layout to the steady-state temperature field without labeled data, which equals solving an entire family of partial difference equations (PDEs). To realize the physics-guided training without labeled data, we employ the heat conduction equation and finite difference method to construct the loss function. Since the solution is sensitive to boundary conditions, we properly impose hard constraints by padding in the Dirichlet and Neumann boundary conditions. In addition, the neural network architecture is well-designed to improve the prediction precision of the problem at hand, and pixel-level online hard example mining is introduced to overcome the imbalance of optimization difficulty in the computation domain. The experiments

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FEA-Net: A physics-guided data-driven model for efficient mechanical response prediction

Cited by 64 publications

References 40 publications

Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network

Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network

Explainable Artificial Intelligence for Mechanics: Physics-Explaining Neural Networks for Constitutive Models

Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data

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