Rapid and Precise Topological Comparison with Merge Tree Neural Networks

Area of Science:

• Scientific Visualization
• Topological Data Analysis
• Machine Learning

Background:

• Merge trees are crucial for scalar field visualization but comparisons are computationally intensive.
• Existing methods rely on exhaustive node matching, limiting efficiency.

Purpose of the Study:

• To develop a computationally efficient and accurate method for merge tree comparison.
• To introduce the Merge Tree Neural Network (MTNN) for rapid similarity computation.

Main Methods:

• Utilized graph neural networks to generate vector embeddings of merge trees.
• Developed the MTNN model incorporating topological attention for enhanced similarity.
• Trained and validated the model on real-world datasets across various domains.

Main Results:

• The MTNN achieves high-quality similarity computation for merge trees.
• Demonstrated significant speedup (over 100×) compared to prior state-of-the-art methods.
• Maintained a low error rate (<0.1%) on benchmark datasets.

Conclusions:

• The MTNN offers a superior approach for merge tree comparison in terms of accuracy and efficiency.
• The model shows generalizability across diverse datasets.
• This advancement facilitates more effective scientific visualization and data analysis.