For large systems of PDE one approach to numerically approximate the solution is to use Galerkin decomposition. This approach separates time and space components. One further step could be to restrict the number of components in the obtained sum. The basis functions can be obtained by using the approach "Sampling weights of Deep Neural Networks" developed by the research group under supervision of Dr. Felix Dietrich. However, the basis functions obtained this way might not be orthogonal. As a result, the matrix of the obtained linear differential equation for the coefficients is not sparse and might have a high condition number leading to difficulties when computing the inverse.
The goal of this project is to investigate which methods can be applied to large systems of linear DAE.