Rapid and Precise Topological Comparison with Merge Tree Neural Networks

Merge trees are a valuable tool in scientific visualization of scalar fields; however, current methods for merge tree comparisons are computationally expensive, primarily due to the exhaustive matching between tree nodes. To address this challenge, we introduce the merge tree neural networks (MTNN), a learned neural network model designed for merge tree comparison. The MTNN enables rapid and high-quality similarity computation. We first demonstrate how graph neural networks (GNNs), which emerged as an effective encoder for graphs, can be trained to produce embeddings of merge trees in vector spaces that enable efficient similarity comparison. Next, we formulate the novel MTNN model that further improves the similarity comparisons by integrating the tree and node embeddings with a new topological attention mechanism. We demonstrate the effectiveness of our model on real-world data in different domains and examine our model's generalizability across various datasets. Our experimental analysis demonstrates our approach's superiority in accuracy and efficiency. In particular, we speed up the prior state-of-the-art by more than 100x on the benchmark datasets while maintaining an error rate below 0.1%.