Title: Physical System Design Using Hamiltonian Monte Carlo over Learned Manifolds. Abstract: The design of complex physical systems entails satisfying several competing performance objectives. In practice, some design requirements are often implicit in the intuition and knowledge of designers who have many years of experience working with similar designs. Designers use this experience to sample a few promising candidates in the design space and evaluate or simulate them using detailed, typically slow multiphysics models. The goal in design is usually to generate a diverse set of high-performing design configurations that allow trade-offs across different objectives and avoid early concretization. In this paper, we develop a machine learning approach to automate physical system design. We use deep generative models to learn a manifold of the valid design space, followed by Hamiltonian Monte Carlo (HMC) with simulated annealing to explore and optimize design over the learned manifold, producing a diverse set of optimal designs. Our approach is akin to partial simulated annealing restricted to the learned design manifold, where the annealing schedule is varied to trade-off different objectives. To prevent our approach from traversing off the design manifold and proposing unreliable designs, we leverage Monte Carlo dropout as a way to detect and avoid design configurations where the learned model cannot be trusted. We demonstrate the efficacy of our proposed approach using several case studies that include the design of an SAE race vehicle, propeller, and air vehicle. Across these case studies, we successfully show how our method generates high-performing and diverse designs. 