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

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

Journal Article · 01 February 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;

Not Available

View Accepted Manuscript (Publisher)

Cite

Export

Save

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 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

Similar Records

Generalizable Framework of Unpaired Domain Transfer and Deep Learning for the Processing of Real-Tim

Journal Article · 2022 · Phys. Rev. Appl. · OSTI ID:1856363

Tang, Kunning; Wang, Ying Da; McClure, James; +3 more

Solving electrical impedance tomography with deep learning

Journal Article · 2020 · Journal of Computational Physics · OSTI ID:1775905

Fan, Yuwei; Ying, Lexing

A performance spectrum for parallel computational frameworks that solve PDEs

Journal Article · 2017 · Concurrency and Computation. Practice and Experience · OSTI ID:1414485

Chang, J.; Nakshatrala, K. B.; Knepley, M. G.; +1 more

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

Citation Formats

References (45)

Similar Records

Related Subjects