A continuing problem in generating spatial fields of data concerns the “dropping out” of data within a field's prescribed extent due to instrument failure or natural interference, and then interpolating reasonable values to fill in these missing sections. A complete portrait of current-fields on the ocean can, for example, improve the odds of rescue crews successfully locating cargo or passengers lost overboard, or containing oil spills. Linear interpolations, although among the simplest and most direct potential solutions, are of limited utility as they can often lead to unrealistic results. Use of neural network models in these situations has seen some success, as they are adaptive and nonlinear, and can be applied in very different environments to work with various forms of numerical data. Given a general definition of a spatial field as a highly self-correlated numerical surface representing a particular measurable attribute over a defined space, a specific category of neural network is proposed as a means of accurately interpolating missing values within a field. A test-case field of two-dimensional velocity vectors of surface ocean currents within the Gulf of Maine was chosen, where varying ionospheric conditions interfered with radar-based current sensors. Neural networks trained to approximate the hourly first-derivative temporal velocity-surface of the currents of the Gulf were found to correctly fill in missing points in a time series with a correlation of up to 0.95 when applied to a single location, and a correlation of 0.70 - 0.90 on a gulf-wide basis. Further refinement by assigning distinct neural models to subregions of the gulf is expected to improve further upon these results.