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DL-PDE prescribes a way to feed a neural network data, which in turn comes up with a PDE of the form

$$u_{t}(t,x,y) = F(x,y,u,u_{x},u_{y},u_{xx},u_{xy},u_{yy},...) \hspace{0.5cm} (x,y) \in \Omega \subset \mathbb{R}^{2}, t \in [0, T]$$

I am looking for a way to feed a neural network the same data and also prescribe a number of other variables (say 2, making the total number of variables 3), and the neural network could come up with a system of PDE's comprising of three equations with three variables.

Any leads for this?

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    $\begingroup$ Hello, welcome to Artificial Intelligence Stack Exchange. You inserted an image containing an equation. If you are comfortable in keeping the equation using LaTex then please do it. $\endgroup$
    – hanugm
    Nov 5 '21 at 4:31

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