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Enhanced physics-informed neural networks for hyperelasticity
[article]

2022
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arXiv
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pre-print

[23, 24] , and

arXiv:2205.14148v1
fatcat:7ykazsqr2jg6hngieb4uzun4bu
*Abueidda*et al. ... One of the most common and most straightforward optimizers used is gradient descent [39] :*W*c+1 ij =*W*c ij − β ∂ L ∂*W*c ij b c+1 i = b c i − β ∂ L ∂b c i ( 12 ) where β denotes the learning rate. ...##
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Deep Learning Sequence Methods in Multiphysics Modeling of Steel Solidification

2021
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Metals
*

The outputŶ [l] for a layer l is calculated as: [ ] [ ] [ 1] [ ] [ ] [ ] [ ] ( ) l l l l l l l f − = + = Z

doi:10.3390/met11030494
fatcat:vzrnv6xvcnbxpbf4ugncknpe4y
*W*Z b Y Z , (6) Z [l] =*W*[l] Z [l−1] + b [l] Y [l] = f [l] (Z [l] ) , (6) where*W*[l] (n ... Neurons of successive layers are connected through associated weights and biases*W*and b. ...##
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Meshless physics-informed deep learning method for three-dimensional solid mechanics
[article]

2021
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arXiv
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pre-print

One of the most common and most straightforward optimizers used in machine learning is gradient descent, as expressed below:

arXiv:2012.01547v2
fatcat:hcpfovszhfchjedvo3cg6vmjaa
*W*c+1 ij =*W*c ij − β ∂ L ∂*W*c ij b c+1 i = b c i − β ∂ L ∂b c i (2) where β ... Upon initialization, the weights*W*and biases b of the model will be far from ideal. ...##
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Topology optimization of 2D structures with nonlinearities using deep learning
[article]

2020
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arXiv
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pre-print

*Abueidda*et al. ... The goal of the optimization problem is to find the weights

*W*of the network that minimize the loss between the ground-truth (16) where N is the number of training examples. ...

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Surrogate Neural Network Model for Sensitivity Analysis and Uncertainty Quantification of the Mechanical Behavior in the Optical Lens-Barrel Assembly
[article]

2022
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arXiv
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pre-print

*W*k+1 ij =

*W*k ij − γ ∂L ∂

*W*k ij b k+1 i = b k i − γ ∂L ∂b k i (8) Sensitivity and Uncertainty Analyses Sensitivity analysis is used to assess the impact of the perturbation in an input on an output. ... For a layer l, the predicted output Ô[l] is calculated as: Z [l] =

*W*[l] Ô[l−1] + b [l] Ô[l] = f [l] (Z [l] ) (6) where

*W*[l] (n l ×n l−1 ) is a matrix of weights and b [l] (n l−1 ×1) is a vector of biases ...

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A deep learning energy method for hyperelasticity and viscoelasticity
[article]

2022

One of the most prevalent and most straightforward optimizers used is gradient descent [39] :

doi:10.48550/arxiv.2201.08690
fatcat:eiyphovk2jhqzheoespg2mzioq
*W*c+1 ij =*W*c ij − γ ∂ L ∂*W*c ij b c+1 i = b c i − γ ∂ L ∂b c i ( 2 ) where γ represents the learning rate ... For a layer l, the output Ŷ l is calculated as: Z l =*W*l Ŷ l−1 + b l Ŷ l = f l Z l (1) where the weights*W*and biases b are updated after every training pass. ...##
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Exploring the structure-property relations of thin-walled, 2D extruded lattices using neural networks
[article]

2022
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arXiv
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pre-print

*Diab*

*Abueidda*: Supervision, Writing -Review & Editing. Iwona Jasiuk: Supervision, Resources, Writing -Review & Editing, Funding Acquisition. ...

*W*911NF-18-2-0067) and the National Science Foundation grant (MOMS-1926353). ... As investigated by

*Abueidda*et al. ...

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The Merger of Topology Optimisation in Additive Manufacturing

2021
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Zenodo
*

Springer, Cham. https://doi.org/10.1007/978-3-030-79457-6_19 [3]

doi:10.5281/zenodo.5602806
fatcat:puxjmw55pjhjti6g2ydadpqy4m
*Diab**W*.*Abueidda*, Seid Koric, Nahil A. Sobh. ... Design Consideration for Additively Manufactured Components Through Topology Optimization and Generative Design for Weight Reduction. 10.1007/978-981-16-5763-4_49. [2] Almasri*W*., Bettebghor D., Ababsa ...##
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LatticeOPT: A heuristic topology optimization framework for thin-walled, 2D extruded lattices
[article]

2022
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arXiv
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pre-print

*Diab*

*Abueidda*: Supervision, Writing -Review & Editing. Iwona Jasiuk: Supervision, Resources, Writing -Review & Editing, Funding Acquisition. ...

*W*911NF-18-2-0067) and the National Science Foundation grant (MOMS-1926353). ... the lattice design space and design variables Currently, the LatticeOPT framework supports the definition of a cubic lattice design space, defined by the in-plane cross-section length (L) and width (

*W*) ...

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Deep energy method in topology optimization applications
[article]

2022
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arXiv
*
pre-print

M SE ∂Ωu , (11) where

arXiv:2207.03072v1
fatcat:6si3s4srivcwde5bed54wuppua
*w*is a user-defined weight parameter. ... The neurons of consecutive layers are connected by a set of weights*W*and biases b. ...