Quantifying the Worst-Case Projection Error in DC-OPF Proxy Neural Networks
Tekeler, Eren
Tekeler, Eren
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Abstract
Given a proxy NN that predicts DC-OPF solutions, what is the largest minimal projection error needed for feasibility restoration? Quantifying this error over some adversarial set is crucial in safety-critical tasks, as it directly corresponds to the largest correction required to restore the feasibility of a data-driven model prediction. In this study, we formulate the Maximum Projection Error (MPE) problem for DC-OPF as a nonconvex bilevel problem. Since the bilevel formulation is intractable for commercial solvers (i.e., Gurobi), we apply duality-based reduction techniques to obtain a single-level equivalent, with reintroduced primal constraints serving as a dual-unboundedness safety buffer. We solve the problem using Gurobi 13�s spatial branch and bound solver, in conjunction with the Gurobi Machine Learning toolbox, and we integrate the state-of-the-art NN verification technique ?-CROWN to generate valid cuts on the NN output. Global optimality is achieved for 3 and 14- bus systems, while the computational advantages of ?-CROWN bound tightening first emerge at the 14-bus scale; for 37-bus systems, the solver certifies optimality gaps as low as 55%. These results demonstrate that the proposed approach can provide verified upper bounds on worst-case NN feasibility restoration.
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Date
1/1/2026
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Graduate Student
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Poster
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Electrical Engineering
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College of Engineering and Mathematical Sciences
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Engineering