Partial differential equations (or PDEs) are a type of problem that comes up in diverse areas of mathematics and engineering. From the heat equation to the wave equation, they are an obstacle that frequently needs to be tackled. While PDEs in low-dimensional base spaces are mostly well understood, those in high-dimensional base spaces are a lot more complicated yet still common, and require better methods to deal with.

PDEs are not unique in this regard, as problems such as regression, classification, and more also suffer from this so-called "curse of dimensionality", e.g. the difficulty spike while dealing with problems with higher dimensions. Some approaches to this problems are sparse grids and neural nets, both ways of approximating high-dimensional functions in a more efficient way. Sparse grids attempt do accomplish this by describing the function in terms of hierarchical basis functions, and leave out to ones that contribute less to the function sum. Neural nets, similarly approximates the function, but by using parameterized functions instead. Both techniques have been combined in the past as "neural sparse grids" or "deep sparse grids" in order to solve the previously mentioned problems. This thesis will attempt to use the same approach on PDEs, as part of the currently developed deep sparse grids codebase.