The increase of renewable energy, combined with the increased vulnerability of critical infrastructure to natural and human disasters, requires efficient simulation and optimization of energy system operations. In addition, coordination of multiple technologies requires seamless bridging of vastly different time scales. In this talk, we outline our efforts to use physics-informed machine learning in a principled manner to accelerate steady-state optimization and market clearing in power systems and dynamic transient simulation in natural gas systems. We also offer some thoughts about how to couple these technologies towards higher-fidelity simulation and more strategic day-ahead and real-time decision making. The two main problems considered are DC-Optimal Power Flow, to which we apply active set learning, and Unit Commitment of dual-fuel generators, which we model as a Markov Decision Process. Finally, we opine on the role that emerging generative AI tools may play in advancing this work.