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I am trying to solve a mapping problem on a grid (100x100) where I have few points, say 10, where I know the values of a tensor $\boldsymbol{M}$. I have a scalar field, $v$, which is related to the tensor field. By related I mean, if the values of $\boldsymbol{M}$ is given at each node on the grid, you can get the exact value of $v$ at each node by solving a PDE. I want to train a model to predict $v$ on the grid based on those 10 values of $\boldsymbol{M}$. Is it possible to do so using neural networks? If so, which kind of network should I begin to play with? Any relevant literature would be appreciated.

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