🍩 Database of Original & Non-Theoretical Uses of Topology

(found 6 matches in 0.00208s)

  1. Topological Data Analysis and Machine Learning for Recognizing Atmospheric River Patterns in Large Climate Datasets (2019)

    Grzegorz Muszynski, Karthik Kashinath, Vitaliy Kurlin, Michael Wehner, Prabhat
    Abstract Identifying weather patterns that frequently lead to extreme weather events is a crucial first step in understanding how they may vary under different climate change scenarios. Here, we propose an automated method for recognizing atmospheric rivers (ARs) in climate data using topological data analysis and machine learning. The method provides useful information about topological features (shape characteristics) and statistics of ARs. We illustrate this method by applying it to outputs of version 5.1 of the Community Atmosphere Model version 5.1 (CAM5.1) and the reanalysis product of the second Modern-Era Retrospective Analysis for Research and Applications (MERRA-2). An advantage of the proposed method is that it is threshold-free – there is no need to determine any threshold criteria for the detection method – when the spatial resolution of the climate model changes. Hence, this method may be useful in evaluating model biases in calculating AR statistics. Further, the method can be applied to different climate scenarios without tuning since it does not rely on threshold conditions. We show that the method is suitable for rapidly analyzing large amounts of climate model and reanalysis output data.

  2. Topological Data Analysis: Concepts, Computation, and Applications in Chemical Engineering (2021)

    Alexander D. Smith, Paweł Dłotko, Victor M. Zavala
    Abstract A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g., convolutional neural nets, Fourier series). Topological Data Analysis (TDA) is a field of mathematics that analyzes data from a fundamentally different perspective. TDA represents datasets as geometric objects and provides dimensionality reduction techniques that project such objects onto low-dimensional descriptors. The key properties of these descriptors (also known as topological features) are that they provide multiscale information and that they are stable under perturbations (e.g., noise, translation, and rotation). In this work, we review the key mathematical concepts and methods of TDA and present different applications in chemical engineering.

  3. SuPerPoV: Score and Evolution of the Stratospheric Polar Vortex via Persistent Homology (2026)

    Jake Cordes, Barbara Giunti, Zheng Wu
    Abstract Classifying the stratospheric polar vortex provides predictability for surface weather on extended-range timescales definitions of these events proposed in over 60 years of study depend on empirically chosen parameters and yield different results when one of them changes. Moreover, as previous definitions are based on static thresholds, it is not straightforward to use them to study the spatiotemporal evolution of the vortexe introduce SuPerPoV, a score system that computes displacement and split ratiossing tools from applied topology. The computation is entirely threshold-free, open source, and does not require familiarity with applied topology. The scores generally recovers previous definitions and are output for a user-defined number of days, thus showing the evolution of the event. SuPerPoV offers a paradigm shift in the study of the polar vortex, hopefully bringing a deeper understanding of the polar vortex and related extreme events, such as sudden stratospheric warmings.

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  5. Topology-Preserving Terrain Simplification (2020)

    Ulderico Fugacci, Michael Kerber, Hugo Manet
    Abstract We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operations are edge flips and removals of interior vertices, re-triangulating the link of the removed vertex. This problem is motivated by topological terrain simplification, which means removing as many critical vertices of a terrain as possible while maintaining geometric closeness to the original surface. Existing methods manage to reduce the maximal possible number of critical vertices, but increase thereby the number of regular vertices. Our method can be used to post-process a simplified terrain, drastically reducing its size and preserving its favorable properties.

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  6. Rapid and Precise Topological Comparison With Merge Tree Neural Networks (2024)

    Yu Qin, Brittany Terese Fasy, Carola Wenk, Brian Summa
    Abstract Merge trees are a valuable tool in the 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 Network (MTNN), a learned neural network model designed for merge tree comparison. The MTNN enables rapid and high-quality similarity computation. We first demonstrate how to train graph neural networks, which emerged as effective encoders for graphs, in order to produce embeddings of merge trees in vector spaces for 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 \$100\times\$ on the benchmark datasets while maintaining an error rate below \$0.1\%\$.