Finding the inverse of a matrix with neural networks I have a generic matrix A which is symmetric, positive definite and sparsely populated (it's also quite big, say composed of tens to hundreds thousands rows). I would like to have a neural network learn how to find a matrix B that resembles the inverse of A (ie: that multiplied by A will yeld a minimal spread of the spectral radius) as accurately and as fast as possible.

I was wondering if there are some AI branches that are focused on this kind of problems or if not how could I approach it.

I know the classical algorithms used to do this, but I would just like to have a look at the possibilities offered by machine learning on the subject.
In general this problem falls under the umbrella of "structured prediction" since you are trying to estimate a number of things that are related by virtue of being embedded in a PSD matrix.

Instead of estimating the inverse in one swoop, I'd pick an appropriate algorithm, say inversion by eigendecomposition, estimate the components (eigenvalues and eigenvectors), then piece them together. Here's one paper that shows how: Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix.

Alternatively, you can investigate approximation algorithms such as the one elaborated in Approximating the inverse of a symmetric positive definite matrix

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