The illustration of NORM. (A) Operators defined on Riemannian manifolds, where the input function and output function can be defined on the same or different Riemannian manifolds. The example for this illustration is the operator learning problem of the composite curing case, where the input temperature function and the output deformation function are both defined on the same manifold, the composite part. (B) The framework of NORM, consists of two feature mapping layers (P and Q) and multiple L-layers. (C) The structure of L-layer, consists of the encoder-approximator-decoder block, the linear transformation, and the non-linear activation function. (D) Laplace-Beltrami operator (LBO) eigenfunctions for the geometric domain (the composite part).