  Topological features based on persistent homology capture high-order
structural information so as to augment graph neural network methods. However,
computing extended persistent homology summaries remains slow for large and
dense graphs and can be a serious bottleneck for the learning pipeline.
Inspired by recent success in neural algorithmic reasoning, we propose a novel
graph neural network to estimate extended persistence diagrams (EPDs) on graphs
efficiently. Our model is built on algorithmic insights, and benefits from
better supervision and closer alignment with the EPD computation algorithm. We
validate our method with convincing empirical results on approximating EPDs and
downstream graph representation learning tasks. Our method is also efficient;
on large and dense graphs, we accelerate the computation by nearly 100 times.
