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Enhanced physics-informed neural networks for hyperelasticity
[article]
2022
arXiv
pre-print
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[23, 24] , and 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. ...
arXiv:2205.14148v1
fatcat:7ykazsqr2jg6hngieb4uzun4bu
Deep Learning Sequence Methods in Multiphysics Modeling of Steel Solidification
2021
Metals
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The outputŶ [l] for a layer l is calculated as: [ ] [ ] [ 1] [ ] [ ] [ ] [ ] ( ) l l l l l l l f − = + = Z 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. ...
doi:10.3390/met11030494
fatcat:vzrnv6xvcnbxpbf4ugncknpe4y
Meshless physics-informed deep learning method for three-dimensional solid mechanics
[article]
2021
arXiv
pre-print
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One of the most common and most straightforward optimizers used in machine learning is gradient descent, as expressed below: 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. ...
arXiv:2012.01547v2
fatcat:hcpfovszhfchjedvo3cg6vmjaa
Topology optimization of 2D structures with nonlinearities using deep learning
[article]
2020
arXiv
pre-print
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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. ...
arXiv:2002.01896v4
fatcat:66egnxngrraf5grakwwcxivyde
Surrogate Neural Network Model for Sensitivity Analysis and Uncertainty Quantification of the Mechanical Behavior in the Optical Lens-Barrel Assembly
[article]
2022
arXiv
pre-print
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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 ...
arXiv:2201.09659v1
fatcat:imdzwtsecvapvhbtcg4z3be6iu
A deep learning energy method for hyperelasticity and viscoelasticity
[article]
2022
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One of the most prevalent and most straightforward optimizers used is gradient descent [39] : 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. ...
doi:10.48550/arxiv.2201.08690
fatcat:eiyphovk2jhqzheoespg2mzioq
Exploring the structure-property relations of thin-walled, 2D extruded lattices using neural networks
[article]
2022
arXiv
pre-print
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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. ...
arXiv:2205.06761v1
fatcat:fcgpp5r2pzb2haen2zapg4qezm
The Merger of Topology Optimisation in Additive Manufacturing
2021
Zenodo
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Springer, Cham. https://doi.org/10.1007/978-3-030-79457-6_19 [3] 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 ...
doi:10.5281/zenodo.5602806
fatcat:puxjmw55pjhjti6g2ydadpqy4m
LatticeOPT: A heuristic topology optimization framework for thin-walled, 2D extruded lattices
[article]
2022
arXiv
pre-print
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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) ...
arXiv:2205.14832v1
fatcat:fsntztcyrrfejga2orflkw4sji
Deep energy method in topology optimization applications
[article]
2022
arXiv
pre-print
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M SE ∂Ωu , (11) where w is a user-defined weight parameter. ...
The neurons of consecutive layers are connected by a set of weights W and biases b. ...
arXiv:2207.03072v1
fatcat:6si3s4srivcwde5bed54wuppua