Accuracy of solutions of differential equations with DeepXDE

Question

We used DeepXDE for solving differential equations. (DeepXDE is a framework for solving differential equations, based on TensorFlow). It works fine, but the accuracy of the solution is limited, and optimizing the meta-parameters did not help. Is this limitation a well-known problem? How the accuracy of solutions can be increased? We used the Adam-optimizer; are there optimizers that are more suitable for numerical problems, if high precision is needed?

(I think the problem is not specific for some concrete equation, but if needed I add an example.)

user_6115152 · Answer

There are actually some methods that could increase the accuracy of the model:

Random Resampling
Residual Adaptive Refinement (RAR): https://arxiv.org/pdf/1907.04502.pdf

They even have an implemented example in their github repository:

https://github.com/lululxvi/deepxde/blob/master/examples/Burgers_RAR.py

Also, You could try using a different architecture such as Multi-Scale Fourier NNs. They seem to outperform PINNs, in cases where the solution contains lots of "spikes".

Accuracy of solutions of differential equations with DeepXDE

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