Mosaic flows: A transferable deep learning framework for solving PDEs on unseen domains

Wang, Hengjie; Planas, Robert; Chandramowlishwaran, Aparna; Bostanabad, Ramin

doi:10.1016/j.cma.2021.114424

Mosaic flows: A transferable deep learning framework for solving PDEs on unseen domains

Journal Article · Tue Feb 01 00:00:00 EST 2022 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.114424· OSTI ID:1837379

Wang, Hengjie; ; Chandramowlishwaran, Aparna;

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Sponsoring Organization:: USDOE Advanced Research Projects Agency - Energy (ARPA-E)

Grant/Contract Number:: AR0001209

OSTI ID:: 1837379

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 389; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (45)

Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates Brakkee, E.; Wesseling, P.; Kassels, C. G. M. International Journal for Numerical Methods in Fluids, Vol. 32, Issue 2 https://doi.org/10.1002/(SICI)1097-0363(20000130)32:2<141::AID-FLD877>3.0.CO;2-2	journal	January 2000
An Overlapping Schwarz Method for Spectral Element Solution of the Incompressible Navier–Stokes Equations Fischer, Paul F. Journal of Computational Physics, Vol. 133, Issue 1 https://doi.org/10.1006/jcph.1997.5651	journal	May 1997
U-Net: Convolutional Networks for Biomedical Image Segmentation Ronneberger, Olaf; Fischer, Philipp; Brox, Thomas Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III https://doi.org/10.1007/978-3-319-24574-4_28	book	November 2015
On the limited memory BFGS method for large scale optimization Liu, Dong C.; Nocedal, Jorge Mathematical Programming, Vol. 45, Issue 1-3 https://doi.org/10.1007/BF01589116	journal	August 1989
Prediction of aerodynamic flow fields using convolutional neural networks Bhatnagar, Saakaar; Afshar, Yaser; Pan, Shaowu Computational Mechanics, Vol. 64, Issue 2 https://doi.org/10.1007/s00466-019-01740-0	journal	June 2019
Towards Optimized Schwarz Methods for the Navier–Stokes Equations Blayo, Eric; Cherel, David; Rousseau, Antoine Journal of Scientific Computing, Vol. 66, Issue 1 https://doi.org/10.1007/s10915-015-0020-9	journal	April 2015
The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems E., Weinan; Yu, Bing Communications in Mathematics and Statistics, Vol. 6, Issue 1 https://doi.org/10.1007/s40304-018-0127-z	journal	February 2018
Approximation capabilities of multilayer feedforward networks Hornik, Kurt Neural Networks, Vol. 4, Issue 2 https://doi.org/10.1016/0893-6080(91)90009-T	journal	January 1991
Reconstruction of 3D Microstructures from 2D Images via Transfer Learning Bostanabad, Ramin Computer-Aided Design, Vol. 128 https://doi.org/10.1016/j.cad.2020.102906	journal	November 2020
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data Sun, Luning; Gao, Han; Pan, Shaowu Computer Methods in Applied Mechanics and Engineering, Vol. 361 https://doi.org/10.1016/j.cma.2019.112732	journal	April 2020
PPINN: Parareal physics-informed neural network for time-dependent PDEs Meng, Xuhui; Li, Zhen; Zhang, Dongkun Computer Methods in Applied Mechanics and Engineering, Vol. 370 https://doi.org/10.1016/j.cma.2020.113250	journal	October 2020
Deep generative modeling for mechanistic-based learning and design of metamaterial systems Wang, Liwei; Chan, Yu-Chin; Ahmed, Faez Computer Methods in Applied Mechanics and Engineering, Vol. 372 https://doi.org/10.1016/j.cma.2020.113377	journal	December 2020
Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering Saha, Sourav; Gan, Zhengtao; Cheng, Lin Computer Methods in Applied Mechanics and Engineering, Vol. 373 https://doi.org/10.1016/j.cma.2020.113452	journal	January 2021
Data-driven learning of nonlocal physics from high-fidelity synthetic data You, Huaiqian; Yu, Yue; Trask, Nathaniel Computer Methods in Applied Mechanics and Engineering, Vol. 374 https://doi.org/10.1016/j.cma.2020.113553	journal	February 2021
Flexible shaping: How learning in small steps helps Krueger, Kai A.; Dayan, Peter Cognition, Vol. 110, Issue 3 https://doi.org/10.1016/j.cognition.2008.11.014	journal	March 2009
Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification Zhu, Yinhao; Zabaras, Nicholas Journal of Computational Physics, Vol. 366 https://doi.org/10.1016/j.jcp.2018.04.018	journal	August 2018
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks Geneva, Nicholas; Zabaras, Nicholas Journal of Computational Physics, Vol. 383 https://doi.org/10.1016/j.jcp.2019.01.021	journal	April 2019
Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks Geneva, Nicholas; Zabaras, Nicholas Journal of Computational Physics, Vol. 403 https://doi.org/10.1016/j.jcp.2019.109056	journal	February 2020
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks Jagtap, Ameya D.; Kawaguchi, Kenji; Karniadakis, George Em Journal of Computational Physics, Vol. 404 https://doi.org/10.1016/j.jcp.2019.109136	journal	March 2020
Data-driven deep learning of partial differential equations in modal space Wu, Kailiang; Xiu, Dongbin Journal of Computational Physics, Vol. 408 https://doi.org/10.1016/j.jcp.2020.109307	journal	May 2020
NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations Jin, Xiaowei; Cai, Shengze; Li, Hui Journal of Computational Physics, Vol. 426 https://doi.org/10.1016/j.jcp.2020.109951	journal	February 2021
A unified deep artificial neural network approach to partial differential equations in complex geometries Berg, Jens; Nyström, Kaj Neurocomputing, Vol. 317 https://doi.org/10.1016/j.neucom.2018.06.056	journal	November 2018
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness Jin, Pengzhan; Lu, Lu; Tang, Yifa Neural Networks, Vol. 130 https://doi.org/10.1016/j.neunet.2020.06.024	journal	October 2020
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy Journal of Fluid Mechanics, Vol. 807 https://doi.org/10.1017/jfm.2016.615	journal	October 2016
Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media Mo, Shaoxing; Zhu, Yinhao; Zabaras, Nicholas Water Resources Research, Vol. 55, Issue 1 https://doi.org/10.1029/2018WR023528	journal	January 2019
Deep learning LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey Nature, Vol. 521, Issue 7553 https://doi.org/10.1038/nature14539	journal	May 2015
Deep learning predicts boiling heat transfer Suh, Youngjoon; Bostanabad, Ramin; Won, Yoonjin Scientific Reports, Vol. 11, Issue 1 https://doi.org/10.1038/s41598-021-85150-4	journal	March 2021
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators Lu, Lu; Jin, Pengzhan; Pang, Guofei Nature Machine Intelligence, Vol. 3, Issue 3 https://doi.org/10.1038/s42256-021-00302-5	journal	March 2021
Deep learning to represent subgrid processes in climate models Rasp, Stephan; Pritchard, Michael S.; Gentine, Pierre Proceedings of the National Academy of Sciences, Vol. 115, Issue 39 https://doi.org/10.1073/pnas.1810286115	journal	September 2018
Deep learning predicts path-dependent plasticity Mozaffar, M.; Bostanabad, R.; Chen, W. Proceedings of the National Academy of Sciences, Vol. 116, Issue 52 https://doi.org/10.1073/pnas.1911815116	journal	December 2019
Predicting the output from a complex computer code when fast approximations are available Kennedy, M. Biometrika, Vol. 87, Issue 1 https://doi.org/10.1093/biomet/87.1.1	journal	March 2000
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems No authors listed IEEE Transactions on Neural Networks, Vol. 6, Issue 4 https://doi.org/10.1109/72.392253	journal	July 1995
Xception: Deep Learning with Depthwise Separable Convolutions Chollet, Francois 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) https://doi.org/10.1109/CVPR.2017.195	conference	July 2017
LSTM: A Search Space Odyssey Greff, Klaus; Srivastava, Rupesh K.; Koutnik, Jan IEEE Transactions on Neural Networks and Learning Systems, Vol. 28, Issue 10 https://doi.org/10.1109/TNNLS.2016.2582924	journal	October 2017
Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design Bostanabad, Ramin; Chan, Yu-Chin; Wang, Liwei Journal of Mechanical Design, Vol. 141, Issue 11 https://doi.org/10.1115/1.4044257	journal	September 2019
METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design Chan, Yu-Chin; Ahmed, Faez; Wang, Liwei Journal of Mechanical Design, Vol. 143, Issue 3 https://doi.org/10.1115/1.4048629	journal	November 2020
Physics-Informed Neural Networks for Heat Transfer Problems Cai, Shengze; Wang, Zhicheng; Wang, Sifan Journal of Heat Transfer, Vol. 143, Issue 6 https://doi.org/10.1115/1.4050542	journal	April 2021
Evolutionary Gaussian Processes Planas, Robert; Oune, Nick; Bostanabad, Ramin Journal of Mechanical Design, Vol. 143, Issue 11 https://doi.org/10.1115/1.4050746	journal	May 2021
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em Science, Vol. 367, Issue 6481 https://doi.org/10.1126/science.aaw4741	journal	January 2020
Iterative Methods by Space Decomposition and Subspace Correction Xu, Jinchao SIAM Review, Vol. 34, Issue 4 https://doi.org/10.1137/1034116	journal	December 1992
fPINNs: Fractional Physics-Informed Neural Networks Pang, Guofei; Lu, Lu; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 41, Issue 4 https://doi.org/10.1137/18M1229845	journal	January 2019
Adaptive neural network-based approximation to accelerate eulerian fluid simulation Dong, Wenqian; Liu, Jie; Xie, Zhen SC '19: The International Conference for High Performance Computing, Networking, Storage, and Analysis, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis https://doi.org/10.1145/3295500.3356147	conference	November 2019
Long Short-Term Memory Hochreiter, Sepp; Schmidhuber, Jürgen Neural Computation, Vol. 9, Issue 8 https://doi.org/10.1162/neco.1997.9.8.1735	journal	November 1997
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations Karniadakis, Ameya D. Jagtap & George Em Communications in Computational Physics, Vol. 28, Issue 5 https://doi.org/10.4208/cicp.OA-2020-0164	journal	June 2020

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