References

  1. F. Chevallier, J. Morcrette, F. Chéruy, and N. A. Scott, “Use of a neural-network-based long-wave radiative-transfer scheme in the ECMWF atmospheric model,” Quart J Royal Meteoro Soc, vol. 126, no. 563, pp. 761–776, Jan. 2000. https://doi.org/10.1002/qj.49712656318

  2. V. M. Krasnopolsky and M. S. Fox-Rabinovitz, “A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components,” Ecological Modelling, vol. 191, no. 1, pp. 5–18, Jan. 2006. https://www.sciencedirect.com/science/article/pii/S0304380005003455

  3. M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational physics, vol. 378, pp. 686–707, 2019. https://www.sciencedirect.com/science/article/pii/S0021999118307125

  4. S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, “Scientific Machine Learning Through Physics- Informed Neural Networks: Where we are and What’s Next,” arXiv preprint arXiv:2201.05624, 2022. https://arxiv.org/abs/2201.05624

  5. J. Burkardt, “Investigating Uncertain Parameters in the Burgers Equation,” Mathematics Department, Ajou University, Suwon, Korea, 2013. https://people.sc.fsu.edu/~jburkardt/presentations/burgers_2013_ajou.pdf

  6. W. Koehrsen, “Overfitting vs. underfitting: A complete example,” Towards Data Science, vol. 405, 2018. http://www.pstu.ac.bd/files/materials/1566949131.pdf

  7. S. Xu, Z. Sun, R. Huang, G. Dilong, G. Yang, and S. Ju, “A practical approach to flow field reconstruction with sparse or incomplete data through physics informed neural network,” Acta Mechanica Sinica, vol. 39, Nov. 2022. https://doi.org/10.1007/s10409-022-22302-x