还有一类机器学习模型叫做PINNS(Physics-informed neural networks ), 模型把PDE嵌入了模型求解，所以要求的基本数据库也就变的更小了，最近有的用来做湍流这些，感觉还是比较有意思的。列了一些最近遇到的参考文献，抛砖引玉：
Raissi, M., Perdikaris, P., & Karniadakis, G. (2017). Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.
Eivazi, H., Tahani, M., Schlatter, P., & Vinuesa, R. (2022). Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations. Physics of Fluids, 34. https://doi.org/10.1063/5.0095270
He, Q., & Tartakovsky, A. (2021). Physics‐Informed Neural Network Method for Forward and Backward Advection‐Dispersion Equations. Water Resources Research, 57. https://doi.org/10.1029/2020WR029479