Test Time Training for AC Power Flow Surrogates via Physics and Operational Constraint Refinement
Panteleimon Dogoulis, Mohammad Iman Alizadeh, Sylvain Kubler, Maxime Cordy
TL;DR
ML-based AC power flow surrogates offer speed but risk violating physical constraints under unseen conditions. The paper introduces physics-informed test-time training (PI-TTT), which refines surrogate predictions at inference by solving a self-supervised objective that enforces AC PF equations and operational limits, updating only a small subset of parameters. Across IEEE 14/118/300 and PEGASE 1354-bus systems, PI-TTT achieves 1–2 order-of-magnitude reductions in power-mismatch residuals and constraint violations while preserving fast inference. This approach narrows the gap between fast ML surrogates and traditional solvers, enabling scalable, physically reliable real-time power system analysis and offering warm-start potential for Newton-Raphson refinements.
Abstract
Power Flow (PF) calculation based on machine learning (ML) techniques offer significant computational advantages over traditional numerical methods but often struggle to maintain full physical consistency. This paper introduces a physics-informed test-time training (PI-TTT) framework that enhances the accuracy and feasibility of ML-based PF surrogates by enforcing AC power flow equalities and operational constraints directly at inference time. The proposed method performs a lightweight self-supervised refinement of the surrogate outputs through few gradient-based updates, enabling local adaptation to unseen operating conditions without requiring labeled data. Extensive experiments on the IEEE 14-, 118-, and 300-bus systems and the PEGASE 1354-bus network show that PI-TTT reduces power flow residuals and operational constraint violations by one to two orders of magnitude compared with purely ML-based models, while preserving their computational advantage. The results demonstrate that PI-TTT provides fast, accurate, and physically reliable predictions, representing a promising direction for scalable and physics-consistent learning in power system analysis.