This work presents a method to compute continuous low-thrust fuel-optimal guidance updates on board a spacecraft using a combination of deep learning and differential algebraic techniques. In order to create the large datasets necessary to train neural networks, we also propose a new method using polynomial maps, which provide fuel-optimal guidance updates for any state deviation from a nominal. Constructing the map at the initial time allows the generation of an arbitrarily high number of optimal trajectories for the database via the simple evaluation of polynomials. A trained deep neural network is then capable of providing continuous guidance updates, for which an interplanetary transfer scenario from Earth to Psyche is chosen for evaluation of the guidance schemes performance. As a neural network cannot generalise the highly complex mapping between state and optimal control policy perfectly, one expects some error in the policy. For sensitive dynamical systems and large flight times, this error may be unsuitable for the mission. We therefore further utilise differential algebraic techniques to refine the output of the neural network into highly accurate fuel-optimal guidance updates via a lightweight and iterative-less mapping procedure, suitable for onboard implementation.