Abstract: In this talk, I will present two works on active learning for multi-fidelity simulations. The first introduces the Recursive Non-Additive (RNA) emulator, a flexible statistical model that integrates multi-fidelity data without assuming an additive structure. Using Gaussian process priors, it captures complex relationships while allowing efficient closed-form computation. We further develop four active learning strategies to balance accuracy and simulation cost. The second work focuses on finite element simulations with a real-valued fidelity parameter. We introduce an adaptive non-stationary kernel to better model simulation outputs and propose a sequential design based on integrated mean squared prediction error (IMSPE) to optimize design points while considering computational costs.