Graph-Structured Kernel Design for Power Flow Learning using Gaussian
  Processes
Parikshit Pareek Deepjyoti Deka Sidhant Misra
This paper presents a physics-inspired graph-structured kernel designed for
power flow learning using Gaussian Process (GP). The kernel, named the
vertex-degree kernel (VDK), relies on latent decomposition of voltage-injection
relationship based on the network graph or topology. Notably, VDK design avoids
the need to solve optimization problems for kernel search. To enhance
efficiency, we also explore a graph-reduction approach to obtain a VDK
representation with lesser terms. Additionally, we propose a novel
network-swipe active learning scheme, which intelligently selects sequential
training inputs to accelerate the learning of VDK. Leveraging the additive
structure of VDK, the active learning algorithm performs a block-descent type
procedure on GP's predictive variance, serving as a proxy for information gain.
Simulations demonstrate that the proposed VDK-GP achieves more than two fold
sample complexity reduction, compared to full GP on medium scale 500-Bus and
large scale 1354-Bus power systems. The network-swipe algorithm outperforms
mean performance of 500 random trials on test predictions by two fold for
medium-sized 500-Bus systems and best performance of 25 random trials for
large-scale 1354-Bus systems by 10%. Moreover, we demonstrate that the proposed
method's performance for uncertainty quantification applications with
distributionally shifted testing data sets.