In terahertz tomography the aim is to compute the (complex) refractive index of a material from measurements which consist of reflections and transmissions of electromagnetic waves in the range of 0.1-10 THz. This is an inverse imaging problem where the underlying mathematical problem is associated with Maxwell's equations and simplifications thereof. For higher frequencies one idea is to neglect the wave character and use geometric optics which leads to the eikonal equation as mathematical model. In that sense we deal with the inverse problem of computing the refractive index from time-of-flight measurements. Using training data which, e.g., consist of probes and associated measure data, to train a neural network, we accelerate the evaluation of the forward operator, i.e. the solution of the eikonal equation, signi ficantly compared to standard techniques such as marching schemes. This leads also to a more efficient solution of the inverse problem itself. We show numerical results using Landweber's method. This is joined work with Clemens Meiser and Anne Wald.