CURRICULUM-TRANSFER-LEARNING BASED PHYSICS-INFORMED NEURAL NETWORKS FOR LONG-TIME SIMULATION OF NONLINEAR WAVE PROPAGATION

Guo Yuan; Fu Zhuojia; Min Jian; Liu Xiaoting; Zhao Haitao

doi:10.6052/0459-1879-23-457

Volume 56 Issue 3

Mar. 2024

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2024 > 56(3): 763-773. > DOI: 10.6052/0459-1879-23-457 CSTR: 32045.14.0459-1879-23-457

Guo Yuan, Fu Zhuojia, Min Jian, Liu Xiaoting, Zhao Haitao. Curriculum-transfer-learning based physics-informed neural networks for long-time simulation of nonlinear wave propagation. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 763-773. DOI: 10.6052/0459-1879-23-457

Citation:

PDF (4515 KB)

CURRICULUM-TRANSFER-LEARNING BASED PHYSICS-INFORMED NEURAL NETWORKS FOR LONG-TIME SIMULATION OF NONLINEAR WAVE PROPAGATION

*.
Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, China
†.
Institute of Science and Technology Research, China Three Gorges Corporation, Beijing 101199, China
**.
College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China

Received Date: September 18, 2023
Accepted Date: December 03, 2023
Available Online: December 04, 2023
Published Date: December 04, 2023

Graphical Abstract

Abstract

Abstract

Due to the computational instability to obtain effective solutions in long-term evolution simulation by using the standard physics-informed neural networks (PINN), this paper develops a curriculum-transfer-learning based physics-informed neural networks (CTL-PINN) for long-term nonlinear wave propagation simulation. In the present CTL-PINN, the original long-term problem is transformed into several short-term sub-problems, and the solving process includes the following three stages. In the initial stage, we employ the standard PINN to obtain the solution of the initial short-term sub-problem, and then in the curriculum learning stage the standard PINN with the training information in the previous step is successively used to solve the problem with time domain extension, and next in the transfer learning stage the standard PINN with the training information in the previous step is successively used to solve the problem with time domain transfer. This improved PINN can avoid obtaining the local optimal solutions by using the standard PINN. Finally, several benchmark examples are used to verify the effectiveness and robustness of the proposed CTL-PINN in the solution of long-term nonlinear wave propagation problems.
- curriculum learning,
- transfer learning,
- physics-informed neural networks,
- wave propagation analysis,
- long time simulation,
- nonlinearity

FullText(HTML)

References (31)

References

[1]	Constantin A. Nonlinear water waves: introduction and overview. Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, 2018, 376(2111): 20170310
[2]	张洪生, 王亚玲. 非均匀水流中非线性波传播的数值模拟. 力学学报, 2007, 23(6): 732-740 (Zhang Hongsheng, Wang Yaling. Numerical simulation of nonlinear wave propagation on non-uniform current. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 732-740 (in Chinese) Zhang Hongsheng, Wang Yaling. Numerical simulation of nonlinear wave propagation on non-uniform current. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 732-740 (in Chinese)
[3]	Roy A, Nehra R, Langrock C, et al. Non-equilibrium spectral phase transitions in coupled nonlinear optical resonators. Nature Physics, 2023, 19(3): 427-434 doi: 10.1038/s41567-022-01874-8
[4]	Quan L, Qian F, Liu X, et al. A nonlinear acoustic metamaterial: Realization of a backwards-traveling second-harmonic sound wave. The Journal of the Acoustical Society of America, 2016, 139(6): 3373-3385 doi: 10.1121/1.4949542
[5]	Tasaketh I, Cen W, Liu B, et al. Nonlinear seismic response of SV wave incident angle and direction to concrete gravity dam. International Journal of Civil Engineering, 2022, 20(12): 1479-1494 doi: 10.1007/s40999-022-00756-7
[6]	Zheng PB, Zhang ZH, Zhang HS, et al. Numerical simulation of nonlinear wave propagation from deep to shallow water. Journal of Marine Science and Engineering, 2023, 11(5): 1003 doi: 10.3390/jmse11051003
[7]	Wang S, Ge Y. Efficient sixth-order finite difference method for the two-dimensional nonlinear wave equation with variable coefficient. Mathematical Sciences, 2022, https://doi.org/10.1007/s40096-022-00498-6
[8]	Li K, Tan Z. A two-grid fully discrete Galerkin finite element approximation for fully nonlinear time-fractional wave equations. Nonlinear Dynamics, 2023, 111(9): 8497-8521 doi: 10.1007/s11071-023-08265-5
[9]	Qianshun C, Shengchang W. Spectral method for solving nonlinear wave equations. Acta Mathematicae Applicatae Sinica, 1984, 1(2): 99-107 doi: 10.1007/BF01669671
[10]	Khurshudyan AZH. Nonlinear Green’s functions for wave equation with quadratic and hyperbolic potentials. Advances in Mathematical Physics, 2018, 2018: 1-9
[11]	Fronk MD, Fang L, Packo P, et al. Elastic wave propagation in weakly nonlinear media and metamaterials: a review of recent developments. Nonlinear Dynamics, 2023, 111(12): 10709-10741 doi: 10.1007/s11071-023-08399-6
[12]	查文舒, 李道伦, 沈路航等. 基于神经网络的偏微分方程求解方法研究综述. 力学学报, 2022, 54(3): 543-556 (Zha Wenshu, Li Daolun, Shen Luhang, et al. Review of neural network-based methods for solving partial differential equations. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 543-556 (in Chinese) Zha Wenshu, Li Daolun, Shen Luhang, et al. Review of neural network-based methods for solving partial differential equations. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 543-556 (in Chinese)
[13]	Sarker IH. Deep learning: A comprehensive overview on techniques, taxonomy, applications and research directions. SN Computer Science, 2021, 2(6): 420 doi: 10.1007/s42979-021-00815-1
[14]	Sarker IH. Machine learning: Algorithms, real-world applications and research directions. SN Computer Science, 2021, 2(3): 160 doi: 10.1007/s42979-021-00592-x
[15]	蒋子超, 江俊扬, 姚清河等. 基于神经网络的差分方程快速求解方法. 力学学报, 2021, 53(7): 1912-1921 (Jiang Zichao, Jiang Junyang, Yao Qinghe, et. al. A fast solver based on deep neural network for difference. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1912-1921 (in Chinese) Jiang Zichao, Jiang Junyang, Yao Qinghe, et. al. A fast solver based on deep neural network for difference. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1912-1921 (in Chinese)
[16]	曹蕾蕾, 朱旺, 武建华等. 基于人工神经网络的声子晶体逆向设计. 力学学报, 2021, 53(7): 1992-1998 (Cao Leilei, Zhu Wang, Wu Jianhua et. al,. Inverse design of phononic crystals by artificial neural networks. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1992-1998 (in Chinese) doi: 10.6052/0459-1879-21-142 Cao Leilei, Zhu Wang, Wu Jianhua et. al,. Inverse design of phononic crystals by artificial neural networks. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(7): 1992-1998 (in Chinese) doi: 10.6052/0459-1879-21-142
[17]	胡震宇, 王子路, 陈坚强等. 基于深度神经网络的横流转捩预测. 力学学报, 2023, 55(1): 38-51 (Hu Zhenyu, Wang Zilu, Chen Jianqiang, et al. Prediction of crossflow transition based on deep neural networks. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 38-51 (in Chinese) doi: 10.6052/0459-1879-22-448 Hu Zhenyu, Wang Zilu, Chen Jianqiang, et al. Prediction of crossflow transition based on deep neural networks. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 38-51 (in Chinese) doi: 10.6052/0459-1879-22-448
[18]	黄钟民, 谢臻, 张易申等. 面内变刚度薄板弯曲问题的挠度−弯矩耦合神经网络方法. 力学学报, 2021, 53(9): 2541-2553 (Huang Zhongmin, Xie Zhen, Zhang Yishen, et al. Deflection-bending moment coupling neural network method for the bending problem of thin plates with in-plane stiffness gradient. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2541-2553 (in Chinese) Huang Zhongmin, Xie Zhen, Zhang Yishen, et al. Deflection-bending moment coupling neural network method for the bending problem of thin plates with in-plane stiffness gradient. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2541-2553 (in Chinese)
[19]	Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019, 378: 686-707 doi: 10.1016/j.jcp.2018.10.045
[20]	Jiang X, Wang D, Chen X, et al. Physics-informed neural network for optical fiber parameter estimation from the nonlinear schrödinger equation. Journal of Lightwave Technology, 2022, 40(21): 7095-7105 doi: 10.1109/JLT.2022.3199782
[21]	Li J, Li B. Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation. Chaos, Solitons & Fractals, 2022, 164: 112712
[22]	Jagtap AD, Kawaguchi K, Karniadakis GE. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Journal of Computational Physics, 2020, 404: 109136 doi: 10.1016/j.jcp.2019.109136
[23]	宋家豪, 曹文博, 张伟伟. FD-PINN: 频域物理信息神经网络. 力学学报, 2023, 55(5): 1195-1205 (Song Jiahao, Cao Wenbo, Zhang Weiwei. FD-PINN: frequency domain physics-informed neural network. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1195-1205 (in Chinese) Song Jiahao, Cao Wenbo, Zhang Weiwei. FD-PINN: frequency domain physics-informed neural network. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1195-1205 (in Chinese)
[24]	Tang Z, Fu Z, Reutskiy S. An extrinsic approach based on physics-informed neural networks for PDEs on surfaces. Mathematics, 2022, 10(16): 2861 doi: 10.3390/math10162861
[25]	汤卓超, 傅卓佳. 基于物理信息的神经网络求解曲面上对流扩散方程. 计算力学学报, 2023, 40(2): 216-222 (Tang Zhuochao, Fu Zhuojia. Physics-informed neural networks for solving convection-diffusion equations on surfaces. Chinese Journal of Computational Mechanics, 2023, 40(2): 216-222 (in Chinese) doi: 10.7511/jslx20211021002 Tang Zhuochao, Fu Zhuojia. Physics-informed neural networks for solving convection-diffusion equations on surfaces. Chinese Journal of Computational Mechanics, 2023, 40(2): 216-222 (in Chinese) doi: 10.7511/jslx20211021002
[26]	Xu W, Lu Y, Wang L. Transfer learning enhanced deepONet for long-time prediction of evolution equations. Proceedings of the AAAI Conference on Artificial Intelligence, 2023, 37(9): 10629-10636 doi: 10.1609/aaai.v37i9.26262
[27]	Meng X, Li Z, Zhang D, et al. PPINN: Parareal physics-informed neural network for time-dependent PDEs. Computer Methods in Applied Mechanics and Engineering, 2020, 370: 113250 doi: 10.1016/j.cma.2020.113250
[28]	Guo J, Yao Y, Wang H, et al. Pre-training strategy for solving evolution equations based on physics-informed neural networks. Journal of Computational Physics, 2023, 489: 112258 doi: 10.1016/j.jcp.2023.112258
[29]	Penwarden M, Jagtap AD, Zhe S, et al. A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions. Journal of Computational Physics, 2023, 493: 112464
[30]	Bengio Y, Louradour J, Collobert R, et al. Curriculum learning//Proceedings of the 26th Annual International Conference on Machine Learning. Montreal Quebec Canada: ACM, 2009: 41-48
[31]	Weiss K, Khoshgoftaar TM, Wang D. A survey of transfer learning. Journal of Big Data, 2016, 3(1): 9 doi: 10.1186/s40537-016-0043-6

[1]	Shi Huiqi, Wang Huiming. THEORETICAL NONLINEAR ANALYSIS OF A BIOMIMETIC TUNABLE LENS DRIVEN BY DIELECTRIC ELASTOMER[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1719-1729. DOI: 10.6052/0459-1879-20-212
[2]	Du Xiuli, Ma Chao, Lu Dechun. NONLINEAR UNIFIED STRENGTH MODEL OF GEOMATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 389-397. DOI: 10.6052/0459-1879-13-312
[3]	Tang Long Wang Hu Li Guangyao. Kriging-HDMR metamodeling technique for nonlinear problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 780-784. DOI: 10.6052/0459-1879-2011-4-lxxb2010-494
[4]	Chen Jianbin Li Jie. Stochastic harmonic function and spectral representations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(3): 505-513. DOI: 10.6052/0459-1879-2011-3-lxxb2010-375
[5]	Yanying Zhao, Jian Xu. Mechanism analysis of delayed nonlinear vibration absorber[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(1): 98-106. DOI: 10.6052/0459-1879-2008-1-2007-078
[6]	LARGE-SCALE NONLINEAR PROBLEM OF ELASTIC SPHERICAL SHELLS SUBJECTED TO CONCENTRATED LOAD[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(2): 231-235. DOI: 10.6052/0459-1879-1997-2-1995-220
[7]	NONLINEAR ANALYSIS OF DYNAMIC STABILITY FOR GENERALLY LAMIN-ARED CIRCULAR CYLINDRICAL THICK SHELLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(5): 624-630. DOI: 10.6052/0459-1879-1995-5-1995-476
[8]	TO THE COMPUTATION OF NONLINEAR CONTROL SYSTEMS APPLlCATION OF THE MULTI-LEVEL SUBSTRUCTURAL METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 239-246. DOI: 10.6052/0459-1879-1994-2-1995-542
[9]	A NONLINEAR CONSTITUTIVE THEORY FOR MIXTURE OFTWO-PHASE FLUIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(1): 82-91. DOI: 10.6052/0459-1879-1991-1-1995-812

Cited By

Cited by

Periodical cited type(5)

1.	陈豪龙，唐欣越，王润华，周焕林，柳占立. 基于物理信息神经网络的多介质非线性瞬态热传导问题研究. 力学学报. 2025(01): 89-102 . 本站查看
2.	苑光耀，王俊淞，赵玄烈，耿敬. 基于PINN的二维剪切流圆柱绕流场重构. 力学学报. 2025(02): 436-452 . 本站查看
3.	韦昌，樊昱晨，周永清，刘欣，李驰，王赫阳. 基于时间权重的物理信息神经网络求解非稳态偏微分方程. 力学学报. 2025(03): 755-766 . 本站查看
4.	王飞龙，胡挺，肖扬帆. 基于物理信息神经网络的水库调度研究. 水电能源科学. 2025(04): 213-216 .
5.	张凌海，周彬，罗毅，冯俊. 物理信息神经网络的一种自适应配置点算法. 力学学报. 2024(10): 3069-3083 . 本站查看

Other cited types(0)

Get Citation

PDF

XML

Article Metrics

Article views (548) PDF downloads (119) Cited by(5)

CURRICULUM-TRANSFER-LEARNING BASED PHYSICS-INFORMED NEURAL NETWORKS FOR LONG-TIME SIMULATION OF NONLINEAR WAVE PROPAGATION

Abstract

References

Related Articles

Cited by

Periodical cited type(5)

Other cited types(0)

Catalog

Article Metrics

Related

Download Center

Author Center

CURRICULUM-TRANSFER-LEARNING BASED PHYSICS-INFORMED NEURAL NETWORKS FOR LONG-TIME SIMULATION OF NONLINEAR WAVE PROPAGATION

Abstract

References

Related Articles

Cited by

Periodical cited type(5)

Other cited types(0)

Catalog

Article Metrics

Related

Download Center

Author Center

Export File

Citation

Format

Content