Abstract: In some embodiments, input convex neural networks are used to model and control complex physical systems. In some embodiments, input convex recurrent neural networks are used to capture temporal behavior of dynamical systems. Optimal controllers may be achieved via solving a convex model predictive control problem. Such models and controllers are useful in controlling many types of complex physical systems, including but not limited to heating, ventilation, and air conditioning (HVAC) systems in order to greatly reduce energy consumption compared to classic linear models and controllers.