Systems and methods for calculating L* in the magnetosphere with essentially the same accuracy as with a physics based model at many times the speed by developing a surrogate trained to be a surrogate for the physics-based model. The trained model can then beneficially process input data falling within the training range of the surrogate model. The surrogate model can be a feedforward neural network and the physics-based model can be the TSK03 model. Operatively, the surrogate model can use parameters on which the physics-based model was based, and/or spatial data for the location where L* is to be calculated. Surrogate models should be provided for each of a plurality of pitch angles. Accordingly, a surrogate model having a closed drift shell can be used from the plurality of models. The feedforward neural network can have a plurality of input-layer units, there being at least one input-layer unit for each physics-based model parameter, a plurality of hidden layer units and at least one output unit for the value of L*.