When the black walnut tree leafs out it blocks the sun and water from plants growing under it. Spring bulbs do well in this situation because they go dormant when the tree leafs out, most perennials don't. You might put pots with shade loving plants under the tree and keep them watered all summer. I know black walnut has alleopathic properties. I don't know what plants are affected by this.

I grow poppies (oriental) which take over as the bluebells finish. Howwever, I have no black walnut (mine are under a dogwood) and it seems to work.

You could try hostas and ferns. I grew them both under a black walnut in a previous house.