Accurate AC-PF prediction under domain shift is critical when models trained on medium-voltage (MV) grids are deployed on high-voltage (HV) networks. Existing physics-informed graph neural solvers typically rely on full fine-tuning for cross-regime transfer, incurring high retraining cost and offering limited control over the stability-plasticity trade-off between target-domain adaptation and source-domain retention. We study parameter-efficient domain adaptation for physics-informed self-attention based GNN, encouraging Kirchhoff-consistent behavior via a physics-based loss while restricting adaptation to low-rank updates. Specifically, we apply LoRA to attention projections with selective unfreezing of the prediction head to regulate adaptation capacity. This design yields a controllable efficiency-accuracy trade-off for physics-constrained inverse estimation under voltage-regime shift. Across multiple grid topologies, the proposed LoRA+PHead adaptation recovers near-full fine-tuning accuracy with a target-domain RMSE gap of $2.6\times10^{-4}$ while reducing the number of trainable parameters by 85.46%. The physics-based residual remains comparable to full fine-tuning; however, relative to Full FT, LoRA+PHead reduces MV source retention by 4.7 percentage points (17.9% vs. 22.6%) under domain shift, while still enabling parameter-efficient and physically consistent AC-PF estimation.

翻译：在域偏移条件下实现精确的交流潮流预测至关重要，特别是当基于中压电网训练的模型部署于高压网络时。现有的物理信息图神经网络求解器通常依赖完全微调实现跨区域迁移，这导致高昂的再训练成本，且难以在目标域适应与源域保持之间实现稳定性与可塑性权衡的精细调控。本研究针对基于物理信息的自注意力图神经网络，探索参数高效的域自适应方法，通过物理约束损失函数促进基尔霍夫一致性行为，同时将自适应过程限制在低秩更新范围内。具体而言，我们在注意力投影层应用LoRA技术，并选择性解冻预测头部以调控自适应能力。该设计为电压区域偏移下的物理约束逆估计问题提供了可控的效率-精度权衡机制。在多种电网拓扑结构上的实验表明，所提出的LoRA+PHead自适应方法以仅14.54%的可训练参数量，实现了接近完全微调的精度，其目标域均方根误差差距仅为$2.6\times10^{-4}$。基于物理的残差项与完全微调结果保持相当；然而相较于完全微调，LoRA+PHead在域偏移下将中压源域保持率降低了4.7个百分点（17.9%对比22.6%），同时仍能实现参数高效且物理一致的交流潮流估计。