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We explore the idea of integrating machine learning (ML) with high performance computing (HPC)-driven simulations to address challenges in using simulations to teach computational science and engineering courses. We demonstrate that a ML surrogate, designed using artificial neural networks, yields predictions in excellent agreement with explicit simulation, but at far less time and computing costs. We develop a web application on nanoHUB that supports both HPC-driven simulation and the ML surrogate methods to produce simulation outputs. This tool is used for both in-classroom instruction and for solving homework problems associated with two courses covering topics in the broad areas of computational materials science, modeling and simulation, and engineering applications of HPC-enabled simulations. The evaluation of the tool via in-classroom student feedback and surveys shows that the ML-enhanced tool provides a dynamic and responsive simulation environment that enhances student learning. The improvement in the interactivity with the simulation framework in terms of real-time engagement and anytime access enables students to develop intuition for the physical system behavior through rapid visualization of variations in output quantities with changes in inputs.