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Published in: Computational Mechanics 3/2023

15-11-2022 | Original Paper

Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue

Authors: Guoxiang Grayson Tong, Daniele E. Schiavazzi

Published in: Computational Mechanics | Issue 3/2023

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Abstract

We propose a data-driven framework to increase the computational efficiency of the explicit finite element method in the structural analysis of soft tissue. An encoder–decoder long short-term memory deep neural network is trained based on the data produced by an explicit, distributed finite element solver. We leverage this network to predict synchronized displacements at shared nodes, minimizing the amount of communication between processors. We perform extensive numerical experiments to quantify the accuracy and stability of the proposed synchronization-avoiding algorithm.

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Literature
1.
go back to reference Aslam M, Riaz O, Mumtaz S, Asif AD (2020) Performance comparison of GPU-based Jacobi solvers using CUDA provided synchronization methods. IEEE Access 8:31792–31812CrossRef Aslam M, Riaz O, Mumtaz S, Asif AD (2020) Performance comparison of GPU-based Jacobi solvers using CUDA provided synchronization methods. IEEE Access 8:31792–31812CrossRef
2.
go back to reference Bakarji J, Champion K, Kutz JN, Brunton SL (2022) Discovering governing equations from partial measurements with deep delay autoencoders. arXiv preprint arXiv:2201.05136 Bakarji J, Champion K, Kutz JN, Brunton SL (2022) Discovering governing equations from partial measurements with deep delay autoencoders. arXiv preprint arXiv:​2201.​05136
3.
go back to reference Bartezzaghi A, Cremonesi M, Parolini N, Perego U (2015) An explicit dynamics GPU structural solver for thin shell finite elements. Comput Struct 154:29–40CrossRef Bartezzaghi A, Cremonesi M, Parolini N, Perego U (2015) An explicit dynamics GPU structural solver for thin shell finite elements. Comput Struct 154:29–40CrossRef
4.
go back to reference Belytschko T, Liu WK, Moran B, Elkhodary K (2014) Nonlinear finite elements for continua and structures. Wiley, HobokenMATH Belytschko T, Liu WK, Moran B, Elkhodary K (2014) Nonlinear finite elements for continua and structures. Wiley, HobokenMATH
5.
6.
go back to reference Brunton SL, Proctor JL, Kutz JN (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci 113(15):3932–3937MathSciNetCrossRefMATH Brunton SL, Proctor JL, Kutz JN (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci 113(15):3932–3937MathSciNetCrossRefMATH
7.
go back to reference Chang B, Chen MM, Haber E, Chi EH (2019) AntisymmetricRNN: a dynamical system view on recurrent neural networks Chang B, Chen MM, Haber E, Chi EH (2019) AntisymmetricRNN: a dynamical system view on recurrent neural networks
9.
go back to reference Chen Z, Churchill V, Wu KL, Xiu DB (2022) Deep neural network modeling of unknown partial differential equations in nodal space. J Comput Phys 449:110782MathSciNetCrossRefMATH Chen Z, Churchill V, Wu KL, Xiu DB (2022) Deep neural network modeling of unknown partial differential equations in nodal space. J Comput Phys 449:110782MathSciNetCrossRefMATH
11.
go back to reference Clough RW, Penzien J (1993) Dynamics of structures. Civil engineering series. McGraw-Hill, New YorkMATH Clough RW, Penzien J (1993) Dynamics of structures. Civil engineering series. McGraw-Hill, New YorkMATH
12.
go back to reference Fu XH, Chang LB, Xiu DB (2020) Learning reduced systems via deep neural networks with memory. J Mach Learn Model Comput 1(2):97CrossRef Fu XH, Chang LB, Xiu DB (2020) Learning reduced systems via deep neural networks with memory. J Mach Learn Model Comput 1(2):97CrossRef
13.
go back to reference Funahashi K, Nakamura Y (1993) Approximation of dynamical systems by continuous time recurrent neural networks. Neural Netw 6(6):801–806CrossRef Funahashi K, Nakamura Y (1993) Approximation of dynamical systems by continuous time recurrent neural networks. Neural Netw 6(6):801–806CrossRef
14.
go back to reference Garnelo M, Rosenbaum D, Maddison C, Ramalho T, Saxton D, Shanahan M, Teh YW, Rezende D, Eslami SMA (Jul 2018) Conditional neural processes. In: Proceedings of the 35th international conference on machine learning, volume 80 of Proceedings of Machine Learning Research, pp 1704–1713. PMLR, 10–15 Garnelo M, Rosenbaum D, Maddison C, Ramalho T, Saxton D, Shanahan M, Teh YW, Rezende D, Eslami SMA (Jul 2018) Conditional neural processes. In: Proceedings of the 35th international conference on machine learning, volume 80 of Proceedings of Machine Learning Research, pp 1704–1713. PMLR, 10–15
15.
go back to reference Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, CambridgeMATH Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, CambridgeMATH
16.
go back to reference He KM, Zhang XY, Ren SQ, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp 770–778 He KM, Zhang XY, Ren SQ, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp 770–778
17.
go back to reference Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780CrossRef Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780CrossRef
18.
go back to reference Hu YH, Zhao T, Xú SX, Xu ZL, Lin LZ (2022) Neural-PDE: a RNN based neural network for solving time dependent PDEs. Commun Inf Syst Hu YH, Zhao T, Xú SX, Xu ZL, Lin LZ (2022) Neural-PDE: a RNN based neural network for solving time dependent PDEs. Commun Inf Syst
19.
go back to reference Hughes TJR (2012) The finite element method: linear static and dynamic finite element analysis. Dover Publications, INC., Mineola Hughes TJR (2012) The finite element method: linear static and dynamic finite element analysis. Dover Publications, INC., Mineola
21.
go back to reference Joldes GR, Wittek A, Miller K (2010) Real-time nonlinear finite element computations on GPU-application to neurosurgical simulation. Comput Methods Appl Mech Eng 199(49–52):3305–3314CrossRefMATH Joldes GR, Wittek A, Miller K (2010) Real-time nonlinear finite element computations on GPU-application to neurosurgical simulation. Comput Methods Appl Mech Eng 199(49–52):3305–3314CrossRefMATH
24.
go back to reference Kaheman K, Kutz JN, Brunton SL (2020) SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics. Proc R Soc A Math Phys Eng Sci 476(2242):20200279MathSciNetMATH Kaheman K, Kutz JN, Brunton SL (2020) SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics. Proc R Soc A Math Phys Eng Sci 476(2242):20200279MathSciNetMATH
25.
go back to reference Kaiser E, Kutz JN, Brunton SL (2021) Data-driven discovery of Koopman Eigenfunctions for control. Mach Learn Sci Technol 2(3):035023CrossRef Kaiser E, Kutz JN, Brunton SL (2021) Data-driven discovery of Koopman Eigenfunctions for control. Mach Learn Sci Technol 2(3):035023CrossRef
27.
go back to reference Kim HJ, Vignon-Clementel IE, Coogan JS, Figueroa CA, Jansen KE, Taylor CA (2010) Patient-specific modeling of blood flow and pressure in human coronary arteries. Ann Biomed Eng 38(10):3195–3209CrossRef Kim HJ, Vignon-Clementel IE, Coogan JS, Figueroa CA, Jansen KE, Taylor CA (2010) Patient-specific modeling of blood flow and pressure in human coronary arteries. Ann Biomed Eng 38(10):3195–3209CrossRef
29.
go back to reference Komatitsch D, Erlebacher G, Göddeke D, Michéa D (2010) High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster. J Comput Phys 229(20):7692–7714MathSciNetCrossRefMATH Komatitsch D, Erlebacher G, Göddeke D, Michéa D (2010) High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster. J Comput Phys 229(20):7692–7714MathSciNetCrossRefMATH
30.
go back to reference Kovacs A, Exl L, Kornell A, Fischbacher J, Hovorka M, Gusenbauer M, Breth L, Oezelt H, Yano M, Sakuma N, Kinoshita A, Shoji T, Kato A, Schrefl T (2022) Conditional physics informed neural networks. Commun Nonlinear Sci Numer Simul 104:106041MathSciNetCrossRefMATH Kovacs A, Exl L, Kornell A, Fischbacher J, Hovorka M, Gusenbauer M, Breth L, Oezelt H, Yano M, Sakuma N, Kinoshita A, Shoji T, Kato A, Schrefl T (2022) Conditional physics informed neural networks. Commun Nonlinear Sci Numer Simul 104:106041MathSciNetCrossRefMATH
31.
go back to reference Kronbichler M, Ljungkvist K (2019) Multigrid for matrix-free high-order finite element computations on graphics processors. ACM Trans Parallel Comput 6(1):1–32CrossRef Kronbichler M, Ljungkvist K (2019) Multigrid for matrix-free high-order finite element computations on graphics processors. ACM Trans Parallel Comput 6(1):1–32CrossRef
33.
go back to reference Kutz JN, Brunton SL, Brunton BW, Proctor JL (2016) Dynamic mode decomposition: data-driven modeling of complex systems. SIAM Kutz JN, Brunton SL, Brunton BW, Proctor JL (2016) Dynamic mode decomposition: data-driven modeling of complex systems. SIAM
35.
go back to reference Lu L, Jin PZ, Pang GF, Zhang ZQ, Karniadakis GE (2021) Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nat Mach Intell 3(3):218–229CrossRef Lu L, Jin PZ, Pang GF, Zhang ZQ, Karniadakis GE (2021) Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nat Mach Intell 3(3):218–229CrossRef
36.
go back to reference Malhotra P, Ramakrishnan A, Anand G, Vig L, Agarwal P, Shroff G (2016) LSTM-based encoder-decoder for multi-sensor anomaly detection Malhotra P, Ramakrishnan A, Anand G, Vig L, Agarwal P, Shroff G (2016) LSTM-based encoder-decoder for multi-sensor anomaly detection
37.
go back to reference McCaslin SE, Shiakolas PS, Dennis BH, Lawrence KL (2012) Closed-form stiffness matrices for higher order tetrahedral finite elements. Adv Eng Softw 44(1):75–79CrossRef McCaslin SE, Shiakolas PS, Dennis BH, Lawrence KL (2012) Closed-form stiffness matrices for higher order tetrahedral finite elements. Adv Eng Softw 44(1):75–79CrossRef
38.
go back to reference Olovsson L, Simonsson K, Unosson M (2005) Selective mass scaling for explicit finite element analyses. Int J Numer Meth Eng 63(10):1436–1445CrossRefMATH Olovsson L, Simonsson K, Unosson M (2005) Selective mass scaling for explicit finite element analyses. Int J Numer Meth Eng 63(10):1436–1445CrossRefMATH
39.
go back to reference Park SH, Kim BD, Kang CM, Chung CC, Choi JW (2018) Sequence-to-sequence prediction of vehicle trajectory via LSTM encoder-decoder architecture. In: 2018 IEEE intelligent vehicles symposium (IV). pp 1672–1678. IEEE Park SH, Kim BD, Kang CM, Chung CC, Choi JW (2018) Sequence-to-sequence prediction of vehicle trajectory via LSTM encoder-decoder architecture. In: 2018 IEEE intelligent vehicles symposium (IV). pp 1672–1678. IEEE
40.
go back to reference Partin L, Geraci G, Rushdi A, Eldred MS, Schiavazzi DE (2022) Multifidelity data fusion in convolutional encoder/decoder networks Partin L, Geraci G, Rushdi A, Eldred MS, Schiavazzi DE (2022) Multifidelity data fusion in convolutional encoder/decoder networks
41.
go back to reference Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin ZM, Gimelshein N, Antiga L et al (2019) Pytorch: an imperative style, high-performance deep learning library. Adv Neural Inf Process Syst 32:8026–8037 Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G, Killeen T, Lin ZM, Gimelshein N, Antiga L et al (2019) Pytorch: an imperative style, high-performance deep learning library. Adv Neural Inf Process Syst 32:8026–8037
42.
43.
go back to reference Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707MathSciNetCrossRefMATH Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707MathSciNetCrossRefMATH
44.
go back to reference Sanchez-Gonzalez A, Godwin J, Pfaff T, Ying R, Leskovec J, Battaglia PW (2020) Learning to simulate complex physics with graph networks. In: Proceedings of the 37th international conference on machine learning. ICML’20. JMLR.org Sanchez-Gonzalez A, Godwin J, Pfaff T, Ying R, Leskovec J, Battaglia PW (2020) Learning to simulate complex physics with graph networks. In: Proceedings of the 37th international conference on machine learning. ICML’20. JMLR.org
45.
go back to reference Schillinger D, Evans JA, Frischmann F, Hiemstra RR, Hsu MC, Hughes TJR (2015) A collocated C0 finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics. Int J Numer Meth Eng 102(3–4):576–631CrossRefMATH Schillinger D, Evans JA, Frischmann F, Hiemstra RR, Hsu MC, Hughes TJR (2015) A collocated C0 finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics. Int J Numer Meth Eng 102(3–4):576–631CrossRefMATH
46.
go back to reference Scovazzi G, Carnes B, Zeng X, Rossi S (2016) A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach. Int J Numer Meth Eng 106(10):799–839 Scovazzi G, Carnes B, Zeng X, Rossi S (2016) A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach. Int J Numer Meth Eng 106(10):799–839
47.
go back to reference Seo J, Schiavazzi DE, Kahn AM, Marsden AL (2020) The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls. Int J Numer Methods Biomed Eng 36(8):e3351 Seo J, Schiavazzi DE, Kahn AM, Marsden AL (2020) The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls. Int J Numer Methods Biomed Eng 36(8):e3351
48.
go back to reference Seo J, Schiavazzi DE, Marsden AL (2019) Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels. Comput Mech 64(3):717–739MathSciNetCrossRefMATH Seo J, Schiavazzi DE, Marsden AL (2019) Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels. Comput Mech 64(3):717–739MathSciNetCrossRefMATH
49.
go back to reference Shea DE, Brunton SL, Kutz JN (2021) SINDy-BVP: sparse identification of nonlinear dynamics for boundary value problems. Phys Rev Res 3:023255CrossRef Shea DE, Brunton SL, Kutz JN (2021) SINDy-BVP: sparse identification of nonlinear dynamics for boundary value problems. Phys Rev Res 3:023255CrossRef
50.
51.
go back to reference Shiakolas PS, Nambiar RV, Lawrence KL, Rogers WA (1992) Closed-form stiffness matrices for the linear strain and quadratic strain tetrahedron finite elements. Comput Struct 45(2):237–242CrossRefMATH Shiakolas PS, Nambiar RV, Lawrence KL, Rogers WA (1992) Closed-form stiffness matrices for the linear strain and quadratic strain tetrahedron finite elements. Comput Struct 45(2):237–242CrossRefMATH
52.
go back to reference Stoter SKF, Nguyen TH, Hiemstra RR, Schillinger D (2022) Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods Stoter SKF, Nguyen TH, Hiemstra RR, Schillinger D (2022) Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods
53.
go back to reference Strbac V, Pierce DM, Vander Sloten J, Famaey N (2017) GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations. Comput Methods Biomech Biomed Engin 20(16):1643–1657CrossRef Strbac V, Pierce DM, Vander Sloten J, Famaey N (2017) GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations. Comput Methods Biomech Biomed Engin 20(16):1643–1657CrossRef
54.
go back to reference Taylor ZA, Cheng M, Ourselin S (2008) High-speed nonlinear finite element analysis for surgical simulation using graphics processing units. IEEE Trans Med Imaging 27(5):650–663CrossRef Taylor ZA, Cheng M, Ourselin S (2008) High-speed nonlinear finite element analysis for surgical simulation using graphics processing units. IEEE Trans Med Imaging 27(5):650–663CrossRef
55.
go back to reference Vlachas PR, Byeon W, Wan ZY, Sapsis TP, Koumoutsakos P (2018) Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc R Soc A Math Phys Eng Sci 474(2213):20170844MathSciNetMATH Vlachas PR, Byeon W, Wan ZY, Sapsis TP, Koumoutsakos P (2018) Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc R Soc A Math Phys Eng Sci 474(2213):20170844MathSciNetMATH
56.
57.
go back to reference Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration technique in general analysis of plates and shells. Int J Numer Meth Eng 3(2):275–290CrossRefMATH Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration technique in general analysis of plates and shells. Int J Numer Meth Eng 3(2):275–290CrossRefMATH
Metadata
Title
Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue
Authors
Guoxiang Grayson Tong
Daniele E. Schiavazzi
Publication date
15-11-2022
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 3/2023
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-022-02248-w

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