An Online Machine Learning Multi-resolution Optimization Framework for Energy System Design Limit of Performance Analysis

Designing reliable integrated energy systems for industrial processes requires optimization and verification models across multiple fidelities, from architecture-level sizing to high-fidelity dynamic operation. However, model mismatch across fidelities obscures the sources of performance loss and complicates the quantification of architecture-to-operation performance gaps. We propose an online, machine-learning-accelerated multi-resolution optimization framework that estimates an architecture-specific upper bound on achievable performance while minimizing expensive high-fidelity model evaluations. We demonstrate the approach on a pilot energy system supplying a 1 MW industrial heat load. First, we solve a multi-objective architecture optimization to select the system configuration and component capacities. We then develop an machine learning (ML)-accelerated multi-resolution, receding-horizon optimal control strategy that approaches the achievable-performance bound for the specified architecture, given the additional controls and dynamics not captured by the architectural optimization model. The ML-guided controller adaptively schedules the optimization resolution based on predictive uncertainty and warm-starts high-fidelity solves using elite low-fidelity solutions. Our results on the pilot case study show that the proposed multi-resolution strategy reduces the architecture-to-operation performance gap by up to 42% relative to a rule-based controller, while reducing required high-fidelity model evaluations by 34% relative to the same multi-fidelity approach without ML guidance, enabling faster and more reliable design verification. Together, these gains make high-fidelity verification tractable, providing a practical upper bound on achievable operational performance.