A finite element reduced‐order model based on adaptive mesh refinement and artificial neural networks

Baiges, Joan; Codina, Ramon; Castañar, Inocencio; Castillo, Ernesto

doi:10.1002/nme.6235

Cited by 47 publications

(20 citation statements)

References 46 publications

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“…Here, the neural network is constructed to determine a suitable bending direction angle, m . Recently, applications of neural networks to the finite element method have been studied [19][20][21].…”

Section: Deep Learning For Estimating the Optimal Bending Directionsmentioning

confidence: 99%

Self-updated four-node finite element using deep learning

2021

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This paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

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Section: Deep Learning For Estimating the Optimal Bending Directionsmentioning

confidence: 99%

Self-updated four-node finite element using deep learning

2021

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“…e external environment is a stimulus, and the behavior of learners is a response. It can be seen that "stimulation" plays an important role, and language is the response after stimulation [17]. What behaviorist learning theory emphasizes is that the length and frequency of stimulation of various language materials play a decisive role in the formation of language habits or language proficiency.…”

Section: Implementation Of English Teaching Ability Evaluationmentioning

confidence: 99%

An English Teaching Ability Evaluation Algorithm Based on Frequency Effect

2021

Mobile Information Systems

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Background. English is one of the courses offered in all colleges and universities. The quality of English teaching is directly related to the quality of talent training and the development of students themselves. “Teaching quality evaluation” specifically refers to the education evaluation with teaching as the evaluation object. It is the core and foundation of the whole education evaluation. Teaching quality evaluation is based on certain teaching objectives and teaching norms and standards, through the systematic detection and assessment of teaching and learning. Evaluate its teaching effect and the degree of realization of teaching objectives, and use scientific and feasible methods to make corresponding value judgments to improve the process of teaching. To improve the accuracy of English teaching ability evaluation, an English teaching ability evaluation algorithm based on frequency effect is proposed. Methods. The paper proposes an English teaching ability evaluation algorithm based on frequency effect. Firstly, it constructs the evaluation index system of English teaching ability, including expert evaluation system, student evaluation system, and teacher evaluation system. Then, the indexes affecting the evaluation of English teaching ability are quantified by fuzzy synthesis, and the evaluation indexes are refined. Finally, the basic principle of frequency effect is analyzed, combined with the convolutional neural network. Results. The convolutional neural network evaluation model is constructed, the teaching ability indicators are input into the model, the final evaluation results are output, and the design of the English teaching ability evaluation algorithm based on frequency effect is completed. Conclusions. The experimental results show that this method has high accuracy and efficiency.

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“…It is worth mentioning that our approach points at solving the PDEs by means of DNNs as an approximation strategy. In that respect, what we propose is different from approaches such as [11]. They use labeled data from numerical simulations (although it could be obtained from experiments, in principle) to help the solution of a Boundary Value Problem in some specific aspect, where detailed knowledge of the phenomena that is being modelled is lacking.…”

Section: Introductionmentioning

confidence: 99%

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

Samaniego

Anitescu

Goswami

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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281

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Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In general, in order to solve PDEs that represent real systems to an acceptable degree, analytical methods are usually not enough. One has to resort to discretization methods. For engineering problems, probably the best known option is the finite element method (FEM). However, powerful alternatives such as mesh-free methods and Isogeometric Analysis (IGA) are also available. The fundamental idea is to approximate the solution of the PDE by means of functions specifically built to have some desirable properties. In this contribution, we explore Deep Neural Networks (DNNs) as an option for approximation. They have shown impressive results in areas such as visual recognition. DNNs are regarded here as function approximation machines. There is great flexibility to define their structure and important advances in the architecture and the efficiency of the algorithms to implement them make DNNs a very interesting alternative to approximate the solution of a PDE. We concentrate in applications that have an interest for Computational Mechanics. Most contributions that have decided to explore this possibility have adopted a collocation strategy. In this contribution, we concentrate in mechanical problems and analyze the energetic format of the PDE. The energy of a mechanical system seems to be the natural loss function for a machine learning method to approach a mechanical problem. As proofs of concept, we deal with several problems and explore the capabilities of the method for applications in engineering.

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A finite element reduced‐order model based on adaptive mesh refinement and artificial neural networks

Cited by 47 publications

References 46 publications

Self-updated four-node finite element using deep learning

Self-updated four-node finite element using deep learning

An English Teaching Ability Evaluation Algorithm Based on Frequency Effect

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

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