DeepXDE: A Deep Learning Library for Solving Differential Equations

@article{Lu2020DeepXDEAD,
  title={DeepXDE: A Deep Learning Library for Solving Differential Equations},
  author={Lu Lu and X. Meng and Zhiping Mao and G. Karniadakis},
  journal={SIAM Rev.},
  year={2020},
  volume={63},
  pages={208-228}
}
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, from… Expand
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References

SHOWING 1-10 OF 62 REFERENCES
Solving high-dimensional partial differential equations using deep learning
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
DGM: A deep learning algorithm for solving partial differential equations
PDE-Net: Learning PDEs from Data
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations
...
1
2
3
4
5
...