Journal of Shandong University(Engineering Science) ›› 2024, Vol. 54 ›› Issue (1): 11-24.doi: 10.6040/j.issn.1672-3961.0.2023.155

• Machine Learning & Data Mining • Previous Articles    

Progressive training strategy of physics-informed neural networks based on curriculum regularization

FAN Lilin1, LIU Shihao1, LI Yuan1,2*, MAO Wentao1,2, CHEN Zongtao1   

  1. 1. College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, Henan, China;
    2. Engineering Lab of Intelligence Business &
    Internet of Things, Xinxiang 453007, Henan, China
  • Published:2024-02-01

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63

CLC Number: 

  • TP181
[1] ALTERMAN Z, KARAL F C. Propagation of elastic waves in layered media by finite difference methods[J]. Bulletin of the Seismological Society of America, 1968, 58(1): 367-398.
[2] KUHLEMEYER R L, LYSMER J. Finite element method accuracy for wave propagation problems[J]. Journal of the Soil Mechanics and Foundations Division, 1973, 99(5): 421-427.
[3] JASAK H. Error analysis and estimation for the finite volume method with applications to fluid flows[D]. London, UK: Imperial College London, 1996.
[4] CHENG A H D, CHENG D T. Heritage and early history of the boundary element method[J]. Engineering Analysis with Boundary Elements, 2005, 29(3): 268-302.
[5] KRIZHEVSKY A, SUTSKEVER I, HINTON G E. Imagenet classification with deep convolutional neural networks[J]. Communications of the ACM, 2017, 60(6): 84-90.
[6] LI H, Deep learning for natural language processing: advantages and challenges[J]. National Science Review, 2018, 5(1): 24-26.
[7] WANG X G, DENG X B, FU Q, et al. A weakly-supervised framework for COVID-19 classification and lesion localization from chest CT[J]. IEEE Transactions on Medical Imaging, 2020, 39(8): 2615-2625.
[8] LI Y, MAO W T, WANG G S, et al. A general-purpose machine learning framework for predicting singular integrals in boundary element method[J]. Engineering Analysis with Boundary Elements, 2020, 117: 41-56.
[9] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 2019, 378: 686-707.
[10] JIANG X C, WANG H, LI Y. A physics-data-driven bayesian method for heat conduction problems[EB/OL].(2021-09-02)[2023-07-03].https://arxiv.org/abs/2109.00996.html
[11] WANG H P, LIU Y, WANG S Z. Dense velocity reconstruction from particle image velocimetry/particle tracking velocimetry using a physics-informed neural network[J]. Physics of Fluids, 2022, 34(1): 017116.
[12] ZENG S J, ZHANG Z, ZOU Q S. Adaptive deep neural networks methods for high-dimensional partial differential equations[J]. Journal of Computational Physics, 2022, 463: 111232.
[13] DONG S C, YANG J L. Numerical approximation of partial differential equations by a variable projection method with artificial neural networks[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 398: 115284.
[14] JAGTAP A D, KAWAGUCHI K J, KARNIADAKIS G E. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks[J]. Journal of Computational Physics, 2020, 404: 109136.
[15] JAGTAP A D, KHARAZMI E, KARNIADAKIS G E. Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 365: 113028.
[16] ZOBEIRY N, HUMFELD K D. A physics-informed machine learning approach for solving heat transfer equation in advanced manufacturing and engineering applications[J]. Engineering Applications of Artificial Intelligence, 2021, 101: 104232.
[17] WANG S F, TENG Y J, PERDIKARIS P. Under-standing and mitigating gradient flow pathologies in physics-informed neural networks[J]. SIAM Journal on Scientific Computing, 2021, 43(5): 3055-3081.
[18] MOSELEY B, MARKHAM A, NISSEN-MEYER T. Finite basis physics-informed neural networks(FBPINNs): a scalable domain decomposition approach for solving differential equations[J]. Advances in Computational Mathematics, 2023, 49(4): 62.
[19] LI J H, CHEN J C, LI B. Gradient-optimized physics-informed neural networks(GOPINNs): a deep learning method for solving the complex modified KdV equation[J]. Nonlinear Dynamics, 2022, 107: 781-792.
[20] KHARAZMI E, ZHANG Z, KARNIADKIS G E. Variational physics-informed neural networks for solving partial differential equations[EB/OL].(2019-11-27)[2023-07-03].https://arxiv.org/abs/1912.00873.html
[21] RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations[J]. Science, 2020, 367(6481): 1026-1030.
[22] LU L, MENG X H, MAO Z P, et al. DeepXDE: a deep learning library for solving differential equations[J]. SIAM Review, 2021, 63(1): 208-228.
[23] XU K, DARVE E. ADCME: learning spatially-varying physical fields using deep neural networks[EB/OL].(2020-11-24)[2023-07-03]. https://arxiv.org/abs/2011.11955.html.
[24] HAGHIGHAT E, JUANES R. SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113552.
[25] KRISHNAPRIYAN A, GHOLAMI A, ZHE S, et al. Characterizing possible failure modes in physics-informed neural networks[J]. Advances in Neural Information Processing Systems, 2021, 34: 26548-26560.
[26] EPELBAUM T. Deep learning: technical introduction[EB/OL].(2017-09-05)[2023-07-03]. https://arxiv.org/abs/1709.01412.html
[27] BAYDIN A G, PEARLMUTTER B A, RADUL A A, et al. Automatic differentiation in machine learning: a survey[J]. Journal of Marchine Learning Research, 2018, 18: 1-43.
[28] BENGIO Y, LOURADOUR J, COLLOBERT R. Curriculum learning[C] // Proceedings of the 26th Annual International Conference on Machine Learning. New York, USA: Association for Computing Machinery, 2009: 41-48.
[29] KINGMA D P, BA J. Adam: a method for stochastic optimization[EB/OL].(2014-12-22)[2023-07-03]. https://arxiv.org/abs/1412.6980.html.
[30] BERAHAS A S, NOCEDAL J, TAKAC M. A multi-batch L-BFGS method for machine learning[J]. Advances in Neural Information Processing Systems, 2016, 29: 1055-1063.
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