Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier–Stokes equations.
- Tim Dockhorn. "A Discussion on Solving Partial Differential Equations using Neural Networks." https://arxiv.org/abs/1904.07200
You can hear me talking about this work and machine learning in general on Ashwin's podcast at https://www.youtube.com/watch?v=3c6YXfgi46Q&t=9s.
A neural network (with two fully connected layers of size 16) for the manufactured Poisson problem (using dataset of 2000 interior and boundary points) can be trained using the following command:
foo@bar:~$ python3 poisson.py -b 2000 -n 2A velocity and a pressure neural network (with two fully connected layers size 16 each) for the Kovasznay problem (using dataset of 4000 interior and boundary points) can be trained using the following command:
foo@bar:~$ python3 kovasznay_flow.py -b 4000 -u 2 -p 2We recommend the following package versions to reproduce the results of the paper
- Tensorflow: 1.12.0
- Numpy: 1.16.1
- Scipy: 1.2.0
- Matplotlib: 3.0.2