Deep Learning for Partial Differential Equations

• Training & testing with different meshgrids
• Adam optimizer + Learning rate scheduler (L-BFGS is better)
• Refinement

• tensorflow < 2.0
• scipy, numpy, matplotlib

python problem_Laplace.py

python problem_HeatEquation.py

python problem_steadyNavierStoke.py

python problem_NavierStokeEstimation.py

[1] Kailai Xu, Bella Shi, Shuyi Yin. 2018. Deep learning for Partial Differential Equations (PDEs). CS230.
[2] Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561, 2017c.
[3] Maziar Raissi, 2018a Deep hidden physics models: deep learning of nonlinear partial differential equations. arXiv:1801.06637.