I do add fertilizer every 2nd or 3rd year about 10 inches deep around the drip line. In addition, walnuts benefit from trace quantities of zinc. If your soil is deficient in zinc, there are two easy remedies which can be applied on the same schedule. I don't think that I ever want that many nuts again in the same year. Nut production across the various cultivars is a bit of a mystery.
Some trees bear a few nuts every year with a major flush of nuts every third or fourth year.
Others bear only every 2nd or 3rd year. I apply fertilizer in early spring in the year in which I guess that the tree is due for heavy production. Guessing wrong about the year in which to add fertilizer does not appear to create any problem. Recreational gardeners with one or more trees cannot avoid a certain amount of pilferage. Some of the methods used in commercial walnut groves simply cannot be applied in urban areas.