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Enhanced physics-informed neural networks for hyperelasticity [article]

Diab W. Abueidda, Seid Koric, Erman Guleryuz, Nahil A. Sobh
2022 arXiv   pre-print
[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

Seid Koric, Diab W. Abueidda
2021 Metals  
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]

Diab W. Abueidda, Qiyue Lu, Seid Koric
2021 arXiv   pre-print
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]

Diab W. Abueidda, Seid Koric, Nahil A. Sobh
2020 arXiv   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.  ... 
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]

Shantanu Shahane, Erman Guleryuz, Diab W Abueidda, Allen Lee, Joe Liu, Xin Yu, Raymond Chiu, Seid Koric, Narayana R Aluru, Placid M Ferreira
2022 arXiv   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  ... 
arXiv:2201.09659v1 fatcat:imdzwtsecvapvhbtcg4z3be6iu

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

Diab W. Abueidda, Seid Koric, Rashid Abu Al-Rub, Corey M. Parrott, Kai A. James, Nahil A. Sobh
2022
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]

Junyan He, Shashank Kushwaha, Diab Abueidda, Iwona Jasiuk
2022 arXiv   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.  ... 
arXiv:2205.06761v1 fatcat:fcgpp5r2pzb2haen2zapg4qezm

The Merger of Topology Optimisation in Additive Manufacturing

A. K. Madan, Srashti Saxena
2021 Zenodo  
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]

Junyan He, Shashank Kushwaha, Diab Abueidda, Iwona Jasiuk
2022 arXiv   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)  ... 
arXiv:2205.14832v1 fatcat:fsntztcyrrfejga2orflkw4sji

Deep energy method in topology optimization applications [article]

Junyan He and Shashank Kushwaha and Charul Chadha and Seid Koric and Diab Abueidda and Iwona Jasiuk
2022 arXiv   pre-print
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