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Description
Learning solution operators in a manner that is independent of discretization and resolution remains a central challenge in data-driven modeling. The latent twins framework addresses this problem by constructing operators in a task-adaptive latent space for inverse problems and differential equations. However, in its classical form, latent twins relies on autoencoder architectures that are tied to fixed discretizations, coupling representation learning to a particular grid or resolution.
We address this limitation by separating state information from coordinate information. The latent variables encode the global system state, while a coordinate-conditioned decoder acts as an evaluation operator that reconstructs the state at arbitrary spatial or temporal locations through a family of linear or nonlinear maps. This viewpoint naturally supports sparse, irregular, and multi-resolution data, and connects latent twins to operator learning and reduced-order modeling perspectives. The resulting framework is well suited for applications in imaging, inverse problems, and the reduced-order modeling of time-dependent systems.