Hybrid solvers for inverse problems in higher dimensions

Deterministic forward solvers are very efficient for differential operators, but struggle with non-local integrals. On the other hand, Monte Carlo methods are well-suited to handling integrals, but are comparatively slow at solving differential operators. We want to formulate a hybrid method which uses each tool for the right job in a coherent way, starting with simple 1D integro-differential equations for proton transport, and working our way up.