Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening

2026-07-13

AI Summary

This work addresses the significant degradation in generalization of AC power flow surrogate models following changes in grid topology. To overcome this limitation, the authors propose an architecture-agnostic, gradient-free in-context whitening method that applies ZCA whitening to transform the output space. Leveraging only the first two moments from a reference topology and a small number of samples from the new topology, the approach rapidly re-estimates whitening parameters without updating model weights. Theoretically, ZCA whitening is shown to be the unique affine whitening transformation preserving the physical coordinate semantics of power system variables. Evaluated under N-1 and N-2 contingencies on IEEE 30-, 118-, and 300-bus systems, the method reduces prediction errors by 6–28× (up to 54× for individual variables), decreases worst-case bus power imbalance by up to 30×, and achieves adaptation speeds 21–34× faster than gradient-based methods, with full support for CPU-parallel execution.

Abstract

Machine-learned surrogates for the AC power flow (ACPF) problem amortize the cost of repeated solves on a fixed network, but lose one to two orders of magnitude of accuracy when a line outage changes the topology. This degradation is an operator shift. The altered admittance matrix changes the input-to-output map, so identical inputs yield a different output distribution. Existing methods correct this with target-topology data and per-topology gradient steps. We ask whether the correction can instead be made statistical and gradient-free. We propose In-Context Whitening (ICW), which trains an ACPF surrogate in an output space whitened by the base topology's first two moments, and adapts it to an unseen N-1 or N-2 topology by re-estimating that whitening from a few hundred solved cases on the new topology. This adaptation is gradient-free, weight-free, and architecture-agnostic. We prove that among affine whiteners the unique choice that preserves the coordinate-wise semantics of the physical output vector is ZCA whitening, so within efficient invertible corrections, two moments are sufficient. Across the IEEE 30-, 118-, and 300-bus systems under N-1 and N-2 contingencies, ICW reduces overall error by 6$\times$ to 28$\times$ over frozen surrogates (up to 54$\times$ per-quantity under N-2) and cuts worst-bus power-balance mismatch by up to 30$\times$, with consistent gains across three backbones. At deployment scale it matches or beats gradient-based adaptation in accuracy while adapting 21$\times$ to 34$\times$ faster, with a cost that parallelizes on commodity CPU cores rather than requiring one GPU per contingency.

Problem

• topology adaptation
• operator shift
• power flow surrogate
• gradient-free adaptation
• AC power flow

Innovation

• In-Context Whitening
• gradient-free adaptation
• topology shift
• ZCA whitening
• power flow surrogate