In this work, DeepONet is employed to construct the solution operator in the emergent space. Let Ω ⊂ R D be a bounded open set in the emergent space, and let F = F(Ω; R dx ) and S = S(Ω; R dy ) be two separable functional spaces for which the mapping is to be learned. Furthermore, assume that Ψ : F → S is a non-linear map arising from the solution of an unknown time-dependent PDE. The objective is to approximate the nonlinear operator Ψ via the following parametric mapping