The computation of Feynman integrals is a crucial problem in high-energy physics. One of the most powerful approaches is the method of differential equations, where the integration is traded for the solution of a system of partial differential equations. In this talk, I present two opposite approaches for the solution of these differential equations. The first approach allows us to express the solution in terms of a basis of special functions which can be evaluated efficiently. This method relies on a certain canonical form of the differential equations, which enables the use of sophisticated mathematical tools. The second approach is instead aimed at differential equations of general form. This novel method is based on the framework of physics-informed deep learning, and allows us to train a deep neural network to approximate the solution using the differential equations themselves as constraints, rather than relying on a large database of reference values