Abstract: Many physical systems governed by partial differential equations (PDEs) exhibit solutions that depend on temporal history or involve dynamics across multiple spatial scales. These complexities are particularly prominent in closure model applications within solid mechanics. Operator learning frameworks present compelling opportunities for surrogate modeling in such contexts, as PDE solution operators naturally map between infinite-dimensional function spaces. Moreover, these approaches remain viable when the underlying closure equations are unknown or intractable, circumventing limitations of equation-dependent methods.