  This paper introduces a methodology designed to augment the inverse design
optimization process in scenarios constrained by limited compute, through the
strategic synergy of multi-fidelity evaluations, machine learning models, and
optimization algorithms. The proposed methodology is analyzed on two distinct
engineering inverse design problems: airfoil inverse design and the scalar
field reconstruction problem. It leverages a machine learning model trained
with low-fidelity simulation data, in each optimization cycle, thereby
proficiently predicting a target variable and discerning whether a
high-fidelity simulation is necessitated, which notably conserves computational
resources. Additionally, the machine learning model is strategically deployed
prior to optimization to compress the design space boundaries, thereby further
accelerating convergence toward the optimal solution. The methodology has been
employed to enhance two optimization algorithms, namely Differential Evolution
and Particle Swarm Optimization. Comparative analyses illustrate performance
improvements across both algorithms. Notably, this method is adaptable across
any inverse design application, facilitating a synergy between a representative
low-fidelity ML model, and high-fidelity simulation, and can be seamlessly
applied across any variety of population-based optimization algorithms.}
