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The Innovation Informatics > 2026 Vol. 2 > No. 2 > 100039
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Bayesian physics-informed neural networks to solve the partial differential equations with noise and incomplete constraints

  • 1.

    Ceyear Technologies Co., Ltd, Qingdao 266555, China

  • 2.

    School of Information Science and Engineering, Shandong University, Qingdao 266237, China

  • 3.

    School of Mathematics and Physics, The University of Queensland, St Lucia 4072, Australia

  • 4.

    School of Sciences, China Pharmaceutical University, Nanjing 210009, China

  • 5.

    Department of Mathematics, Faculty of Science, National University of Singapore, Singapore 119077, Singapore

  • 6.

    School of Mathematical Sciences, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China

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  • Corresponding author: lzhang2012@sjtu.edu.cn
  • Received Date:  January 23, 2026
    Accepted Date:  April 13, 2026
    Published Online:  April 14, 2026
The Innovation Informatics  2(2),  https://doi.org/10.59717/j.xinn-inform.2026.100039  |  Cite this article
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    • REFERENCES
  • [1] Li Z., Qiao Z. and Tang T. (2017). Numerical solution of differential equations: Introduction to finite difference and finite element methods. Cambridge University Press. DOI: 10.1017/9781316678725

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    [2] Raissi M., Perdikaris P. and Karniadakis G. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378:686−707. DOI:10.1016/j.jcp.2018.10.045

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    [3] Yang L., Meng X. and Karniadakis G. (2022). B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. J. Comput. Phys. 425:109913. DOI:10.1016/j.jcp.2020.109913

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    [4] Liu Z., Zhang J., Chen Y., et al. (2025). From physics constraints to trustworthy Bayesian reasoning: Synergies of PINN, iPINN, and iBPINN in Prestack AVO inversion. IEEE Geosci. Remote. 63:1−24. DOI:10.1109/TGRS.2025.3636416

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    [5] Zyphur M.J. and Oswald F.L. (2015). Bayesian estimation and inference: A user's guide J. Manage. 41:390−420. DOI:10.1177/0149206313501200

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  • Cite this article:

    Li X., Wu J., Ning X., et al. (2026). Bayesian physics-informed neural networks to solve the partial differential equations with noise and incomplete constraints. The Innovation Informatics 2:100039. https://doi.org/10.59717/j.xinn-inform.2026.100039
    Li X., Wu J., Ning X., et al. (2026). Bayesian physics-informed neural networks to solve the partial differential equations with noise and incomplete constraints. The Innovation Informatics 2:100039. https://doi.org/10.59717/j.xinn-inform.2026.100039

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