Which neural network to use for mapping a vector of size m to a vector of size n, where n >> m?

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.