Residual/gradient adaptative sampling

[gradureauNice]

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Hello, I am trying to resolve Euler's equations to simulate hydrodynamics shocks. So far when simulating strong
shocks, I still strugle to find an acceptable solution.

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In the litterature, the use of residual/gradient adaptative sampling seems to improve the description of
hydrodynamics shocks. Would it be possible to implement this method in neuralPDE?

references :

• https://www.sciencedirect.com/science/article/pii/S0045782522006260
• https://link.springer.com/article/10.1007/s10483-023-2994-7

Moreover, in the litterature, usually only one neural network having three outputs is trained to solve Euler's equations,
as opposed to NeuralPDE that only proposes using one neural network per quantity. Would it be possible to
enable using only one neural network?

[ChrisRackauckas]

Moreover, in the litterature, usually only one neural network having three outputs is trained to solve Euler's equations,
as opposed to NeuralPDE that only proposes using one neural network per quantity. Would it be possible to
enable using only one neural network?

You could, but it would be really slow unless all of the equations have the same required derivatives, since otherwise it has to compute all combinations of derivatives every time.