Self-Supervised Tuning of Low-Fidelity Optimization Models via High-Fidelity Feedback

Low-fidelity (LF) optimization models are widely used in large-scale operations because they can be solved efficiently and reliably, but they often exhibit systematic errors relative to high-fidelity (HF) formulations that better capture physical and operational constraints. Existing learning-based approaches typically rely on supervised or semi-supervised training with HF solutions, which are expensive to compute and may not align with HF operational objectives. We propose a self-supervised framework that parameterizes LF optimization models directly from HF feedback. The low-fidelity problem is embedded as a differentiable optimization layer and trained end-to-end, while a HF correction problem evaluates its solution and provides gradient information through its dual variables, without requiring HF solution labels. We evaluate the framework on optimal power flow, optimal gas flow, and pooling problems, spanning different sources of low- and high-fidelity mismatch. Across all three applications, the self-supervised approach improves objective quality and feasibility over untuned LF models and generally outperforms semi-supervised training. The learned parameterizations also generalize to unseen operating conditions and, for network applications with up to 30,000 nodes, to systems not encountered during training.