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The potential energy surface (PES) describing the interactions between two or more atoms, molecules, or materials is a fundamental construct that can be used to predict the structures, properties, and dynamics of complex systems throughout biology, chemistry, physics, and materials science. In this work, we explore how patterned magnetostatic interactions can be used in the rational design of PES with targeted features. We first explore the PES design space that is accessible with small patterned magnetic arrays via forward and exhaustive enumeration, and characterize the resulting PES by the number, locations, and depths of the PES critical points. This is followed by a detailed investigation into the inverse problem--identification of magnetic patterns that correspond to PES with predefined features--using simulated annealing Monte Carlo (SA-MC) methods. In doing so, we demonstrate a robust theoretical and …