Rethinking materials simulations: Blending direct numerical simulations with neural operators

Oommen, Vivek; Shukla, Khemraj; Desai, Saaketh; Dingreville, Rémi; Karniadakis, George Em

doi:10.1038/s41524-024-01319-1

Title: Rethinking materials simulations: Blending direct numerical simulations with neural operators

Journal Article · 03 July 2024 · npj Computational Materials

DOI: https://doi.org/10.1038/s41524-024-01319-1 · OSTI ID:2391085

; Shukla, Khemraj; Desai, Saaketh;

;

Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: NA0003525

OSTI ID:: 2391085

Alternate ID(s):: OSTI ID: 2426035

Journal Information:: npj Computational Materials, Journal Name: npj Computational Materials Journal Issue: 1 Vol. 10; ISSN 2057-3960

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (56)

Mechanical neural networks: Architected materials that learn behaviors Lee, Ryan H.; Mulder, Erwin A. B.; Hopkins, Jonathan B. Science Robotics, Vol. 7, Issue 71 https://doi.org/10.1126/scirobotics.abq7278	journal	October 2022
A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems Shukla, Khemraj; Jagtap, Ameya D.; Blackshire, James L. IEEE Signal Processing Magazine, Vol. 39, Issue 1 https://doi.org/10.1109/MSP.2021.3118904	journal	January 2022
Stability of immiscible nanocrystalline alloys in compositional and thermal fields Monti, J. M.; Hopkins, E. M.; Hattar, K. Acta Materialia, Vol. 226 https://doi.org/10.1016/j.actamat.2022.117620	journal	March 2022
Residual-based attention in physics-informed neural networks Anagnostopoulos, Sokratis J.; Toscano, Juan Diego; Stergiopulos, Nikolaos Computer Methods in Applied Mechanics and Engineering, Vol. 421 https://doi.org/10.1016/j.cma.2024.116805	journal	March 2024
Approximation rates of DeepONets for learning operators arising from advection–diffusion equations Deng, Beichuan; Shin, Yeonjong; Lu, Lu Neural Networks, Vol. 153 https://doi.org/10.1016/j.neunet.2022.06.019	journal	September 2022
An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator Mavi, Arda; Bekar, Ali Can; Haghighat, Ehsan Computer Methods in Applied Mechanics and Engineering, Vol. 407 https://doi.org/10.1016/j.cma.2023.115944	journal	March 2023
Operator learning for predicting multiscale bubble growth dynamics Lin, Chensen; Li, Zhen; Lu, Lu The Journal of Chemical Physics, Vol. 154, Issue 10 https://doi.org/10.1063/5.0041203	journal	March 2021
Group Normalization Wu, Yuxin; He, Kaiming Computer Vision – ECCV 2018 https://doi.org/10.1007/978-3-030-01261-8_1	book	January 2018
Physics-informed machine learning Karniadakis, George Em; Kevrekidis, Ioannis G.; Lu, Lu Nature Reviews Physics, Vol. 3, Issue 6 https://doi.org/10.1038/s42254-021-00314-5	journal	May 2021
Understanding and design of metallic alloys guided by phase-field simulations Zhao, Yuhong npj Computational Materials, Vol. 9, Issue 1 https://doi.org/10.1038/s41524-023-01038-z	journal	June 2023
Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads He, Junyan; Koric, Seid; Kushwaha, Shashank Computer Methods in Applied Mechanics and Engineering, Vol. 415 https://doi.org/10.1016/j.cma.2023.116277	journal	October 2023
A deep material network approach for predicting the thermomechanical response of composites Shin, Dongil; Alberdi, Ryan; Lebensohn, Ricardo A. Composites Part B: Engineering, Vol. 272 https://doi.org/10.1016/j.compositesb.2023.111177	journal	March 2024
Machine Learning Surrogate Model for Acceleration of Ferroelectric Phase-Field Modeling Alhada-Lahbabi, Kévin; Deleruyelle, Damien; Gautier, Brice ACS Applied Electronic Materials, Vol. 5, Issue 7 https://doi.org/10.1021/acsaelm.3c00601	journal	July 2023
A neural network for speaker-independent isolated word recognition Yamaguchi, Kouichi; Sakamoto, Kenji; Akabane, Toshio First International Conference on Spoken Language Processing (ICSLP 1990) https://doi.org/10.21437/ICSLP.1990-282	conference	November 1990
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators Mao, Zhiping; Lu, Lu; Marxen, Olaf Journal of Computational Physics, Vol. 447 https://doi.org/10.1016/j.jcp.2021.110698	journal	December 2021
Multi-fidelity Bayesian neural networks: Algorithms and applications Meng, Xuhui; Babaee, Hessam; Karniadakis, George Em Journal of Computational Physics, Vol. 438 https://doi.org/10.1016/j.jcp.2021.110361	journal	August 2021
Learning time-dependent deposition protocols to design thin films via genetic algorithms Desai, Saaketh; Dingreville, Rémi Materials & Design, Vol. 219 https://doi.org/10.1016/j.matdes.2022.110815	journal	July 2022
MultiSOM: Multi-layer Self Organizing Maps for local structure identification in crystalline structures Aquistapace, Franco; Amigo, Nicolás; Troncoso, Javier F. Computational Materials Science, Vol. 227 https://doi.org/10.1016/j.commatsci.2023.112263	journal	August 2023
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets Wang, Sifan; Wang, Hanwen; Perdikaris, Paris Science Advances, Vol. 7, Issue 40 https://doi.org/10.1126/sciadv.abi8605	journal	October 2021
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 3, Issue 5 https://doi.org/10.1016/0893-6080(90)90005-6	journal	January 1990
Cluster-based network modeling—From snapshots to complex dynamical systems Fernex, Daniel; Noack, Bernd R.; Semaan, Richard Science Advances, Vol. 7, Issue 25 https://doi.org/10.1126/sciadv.abf5006	journal	June 2021
Spectral/hp Element Methods for Computational Fluid Dynamics Karniadakis, George; Sherwin, Spencer Oxford University Press https://doi.org/10.1093/acprof:oso/9780198528692.001.0001	book	January 2005
Accelerating phase-field predictions via recurrent neural networks learning the microstructure evolution in latent space Hu, C.; Martin, S.; Dingreville, R. Computer Methods in Applied Mechanics and Engineering, Vol. 397 https://doi.org/10.1016/j.cma.2022.115128	journal	July 2022
U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow Wen, Gege; Li, Zongyi; Azizzadenesheli, Kamyar Advances in Water Resources, Vol. 163 https://doi.org/10.1016/j.advwatres.2022.104180	journal	May 2022
Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows Zanardi, Ivan; Venturi, Simone; Panesi, Marco Scientific Reports, Vol. 13, Issue 1 https://doi.org/10.1038/s41598-023-41039-y	journal	September 2023
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks Wu, Chenxi; Zhu, Min; Tan, Qinyang Computer Methods in Applied Mechanics and Engineering, Vol. 403 https://doi.org/10.1016/j.cma.2022.115671	journal	January 2023
A data-driven surrogate model to rapidly predict microstructure morphology during physical vapor deposition Herman, Elizabeth; Stewart, James A.; Dingreville, Rémi Applied Mathematical Modelling, Vol. 88 https://doi.org/10.1016/j.apm.2020.06.046	journal	December 2020
Artificial Intelligence in Predicting Mechanical Properties of Composite Materials Kibrete, Fasikaw; Trzepieciński, Tomasz; Gebremedhen, Hailu Shimels Journal of Composites Science, Vol. 7, Issue 9 https://doi.org/10.3390/jcs7090364	journal	September 2023
Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation Cho, Kyunghyun; van Merrienboer, Bart; Gulcehre, Caglar Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP) https://doi.org/10.3115/v1/D14-1179	conference	January 2014
Laplace neural operator for solving differential equations Cao, Qianying; Goswami, Somdatta; Karniadakis, George Em Nature Machine Intelligence, Vol. 6, Issue 6 https://doi.org/10.1038/s42256-024-00844-4	journal	June 2024
Trade-offs in the latent representation of microstructure evolution Desai, Saaketh; Shrivastava, Ankit; D’Elia, Marta Acta Materialia, Vol. 263 https://doi.org/10.1016/j.actamat.2023.119514	journal	January 2024
Benchmark problems for the Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) Dingreville, Remi Philippe Michel; Stewart, James Allen; Chen, Elton Y. https://doi.org/10.2172/1729722	report	November 2020
Predicting traction return current in electric railway systems through physics-informed neural networks Kapoor, Taniya; Wang, Hongrui; Nunez, Alfredo 2022 IEEE Symposium Series on Computational Intelligence (SSCI) https://doi.org/10.1109/SSCI51031.2022.10022290	conference	December 2022
Learning deep Implicit Fourier Neural Operators (IFNOs) with applications to heterogeneous material modeling You, Huaiqian; Zhang, Quinn; Ross, Colton J. Computer Methods in Applied Mechanics and Engineering, Vol. 398 https://doi.org/10.1016/j.cma.2022.115296	journal	August 2022
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
Emulating microstructural evolution during spinodal decomposition using a tensor decomposed convolutional and recurrent neural network Wu, Peichen; Iquebal, Ashif Sikandar; Ankit, Kumar Computational Materials Science, Vol. 224 https://doi.org/10.1016/j.commatsci.2023.112187	journal	May 2023
Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks Regazzoni, Francesco; Pagani, Stefano; Salvador, Matteo Nature Communications, Vol. 15, Issue 1 https://doi.org/10.1038/s41467-024-45323-x	journal	February 2024
Phase-Field Models for Microstructure Evolution Chen, Long-Qing Annual Review of Materials Research, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.matsci.32.112001.132041	journal	August 2002
Deep neural operators as accurate surrogates for shape optimization Shukla, Khemraj; Oommen, Vivek; Peyvan, Ahmad Engineering Applications of Artificial Intelligence, Vol. 129 https://doi.org/10.1016/j.engappai.2023.107615	journal	March 2024
Transformer Networks for Trajectory Forecasting Giuliari, Francesco; Hasan, Irtiza; Cristani, Marco 2020 25th International Conference on Pattern Recognition (ICPR) https://doi.org/10.1109/ICPR48806.2021.9412190	conference	January 2021
Learning two-phase microstructure evolution using neural operators and autoencoder architectures Oommen, Vivek; Shukla, Khemraj; Goswami, Somdatta npj Computational Materials, Vol. 8, Issue 1 https://doi.org/10.1038/s41524-022-00876-7	journal	September 2022
Spatiotemporal prediction of microstructure evolution with predictive recurrent neural network Kazemzadeh Farizhandi, Amir Abbas; Mamivand, Mahmood Computational Materials Science, Vol. 223 https://doi.org/10.1016/j.commatsci.2023.112110	journal	April 2023
A framework based on symbolic regression coupled with eXtended Physics-Informed Neural Networks for gray-box learning of equations of motion from data Kiyani, Elham; Shukla, Khemraj; Karniadakis, George Em Computer Methods in Applied Mechanics and Engineering, Vol. 415 https://doi.org/10.1016/j.cma.2023.116258	journal	October 2023
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
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
Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems Tripura, Tapas; Chakraborty, Souvik Computer Methods in Applied Mechanics and Engineering, Vol. 404 https://doi.org/10.1016/j.cma.2022.115783	journal	February 2023
Microstructure morphology and concentration modulation of nanocomposite thin-films during simulated physical vapor deposition Stewart, James A.; Dingreville, Rémi Acta Materialia, Vol. 188 https://doi.org/10.1016/j.actamat.2020.02.011	journal	April 2020
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks Cai, Shengze; Wang, Zhicheng; Lu, Lu Journal of Computational Physics, Vol. 436 https://doi.org/10.1016/j.jcp.2021.110296	journal	July 2021
Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator–regression neural network Yin, Minglang; Ban, Ehsan; Rego, Bruno V. Journal of The Royal Society Interface, Vol. 19, Issue 187 https://doi.org/10.1098/rsif.2021.0670	journal	February 2022
Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods Montes de Oca Zapiain, David; Stewart, James A.; Dingreville, Rémi npj Computational Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41524-020-00471-8	journal	January 2021
FourCastNet: Accelerating Global High-Resolution Weather Forecasting Using Adaptive Fourier Neural Operators Kurth, Thorsten; Subramanian, Shashank; Harrington, Peter Proceedings of the Platform for Advanced Scientific Computing Conference https://doi.org/10.1145/3592979.3593412	conference	June 2023
Electrochemically induced fracture in LLZO: How the interplay between flaw density and electrostatic potential affects operability Monismith, Scott; Qu, Jianmin; Dingreville, Rémi Journal of Power Sources, Vol. 559 https://doi.org/10.1016/j.jpowsour.2023.232646	journal	March 2023
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
Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy Shin, Dongil; Alberdi, Ryan; Lebensohn, Ricardo A. npj Computational Materials, Vol. 9, Issue 1 https://doi.org/10.1038/s41524-023-01085-6	journal	July 2023
Physics-Informed Deep Neural Operator Networks Goswami, Somdatta; Bora, Aniruddha; Yu, Yue Computational Methods in Engineering & the Sciences https://doi.org/10.1007/978-3-031-36644-4_6	book	January 2023
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function Leshno, Moshe; Lin, Vladimir Ya.; Pinkus, Allan Neural Networks, Vol. 6, Issue 6 https://doi.org/10.1016/S0893-6080(05)80131-5	journal	January 1993

Similar Records

Learning two-phase microstructure evolution using neural operators and autoencoder architectures

Journal Article · 2022 · npj Computational Materials · OSTI ID:1885197

Oommen, Vivek; Shukla, Khemraj; Goswami, Somdatta; +2 more

Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

Journal Article · 2021 · Transport in Porous Media · OSTI ID:1785291

Santos, Javier E.; Yin, Ying; Jo, Honggeun; +6 more

Dynamic calibration of differential equations using machine learning, with application to turbulence models

Journal Article · 2022 · Journal of Computational Physics · OSTI ID:1843176

Boureima, Ismael; Gyrya, Vitaliy; Saenz, Juan Antonio; +2 more

Title: Rethinking materials simulations: Blending direct numerical simulations with neural operators

Citation Formats

References (56)

Similar Records

Related Subjects