Neural operators are gaining attention as powerful tools for solving PDEs. However, handling complex geometries remains a challenge, especially in the training phase. This is especially relevant when domain geometry is an input of the neural operator or when the geometry evolves in time. Unfitted/Immersed or Embedded boundary methods have gained attention for allowing simulations in complex domains without requiring boundary-conforming meshes. Such approaches could facilitate the development of neural operators in complex geometries. Nonetheless, many existing methods require ad-hoc modifications to standard Finite Element structures, such as tessellating elements intersected by the embedded boundary, constructing special quadrature rules, or defining geometry-dependent surrogate boundaries. In this talk we present the Generalized Weighted Shifted Boundary Method (G-WSBM), a generalized formulation of the WSBM approach [1], which offers a generalized framework for handling complex geometries in a geometry-agnostic manner. The G-WSBM allows the definition of geometry-parametrized Finite Element spaces, and thus, enables neural operators to efficiently process irregular domains and/or parametric domains. In the talk we will present the formulation and give some examples of its application to the solution of PDEs in complex domains. REFERENCES [1] O. Colomés, A. Main, L. Nouveau and G. Scovazzi (2021). A weighted shifted boundary method for free surface ow problems. Journal of Computational Physics, 424, 109837.