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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 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 100x on the benchmark datasets while maintaining an error rate below 0.1%. 

Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive and limited to specific coordinates. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast. 

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights 

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visualization and analysis pipelines. Although not all topological features present in data are of equal importance. To date, the default definition of feature importance is often assumed and fixed. This work shows how proven explainable deep learning approaches can be adapted for use in topological classification. In doing so, it provides the first technique that illuminates what topological structures are important in each dataset in regards to their class label. In particular, the approach uses a learned metric classifier with a density estimator of the points of a persistence diagram as input. This metric learns how to reweigh this density such that classification accuracy is high. By extracting this weight, an importance field on persistent point density can be created. This provides an intuitive representation of persistence point importance that can be used to drive new visualizations. This work provides two examples: Visualization on each diagram directly and, in the case of sublevel set filtrations on images, directly on the images themselves. This work highlights real-world examples of this approach visualizing the important topological features in graph, 3D shape, and medical image data. 

ABSTRACT We identify the progenitor star of SN 2023ixf in Messier 101 using Keck/NIRC2 adaptive optics imaging and pre-explosion Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS) images. The supernova, localized with diffraction spikes and high-precision astrometry, unambiguously coincides with a progenitor candidate of $$m_\text{F814W}=24.87\pm 0.05$$ (AB). Given its reported infrared excess and semiregular variability, we fit a time-dependent spectral energy distribution (SED) model of a dusty red supergiant (RSG) to a combined data set of HST optical, ground-based near-infrared, and Spitzer Infrared Array Camera (IRAC) [3.6], [4.5] photometry. The progenitor resembles an RSG of $$T_\text{eff}=3488\pm 39$$ K and $$\log (L/\mathrm{L}_\odot)=5.15\pm 0.02$$, with a $$0.13\pm 0.01$$ dex ($$31.1\pm 1.7$$ per cent) luminosity variation at a period of $$P=1144.7\pm 4.8$$ d, obscured by a dusty envelope of $$\tau =2.92\pm 0.02$$ at $$1\, \mu \text{m}$$ in optical depth (or $$A_\text{V}=8.43\pm 0.11$$ mag). The signatures match a post-main-sequence star of $$18.2_{-0.6}^{+1.3}\, \mathrm{M}_\odot$$ in zero-age main-sequence mass, among the most massive SN II progenitor, with a pulsation-enhanced mass-loss rate of $$\dot{M}=(4.32\pm 0.26)\times 10^{-4} \, \mathrm{M}_\odot \, \text{yr}^{-1}$$. The dense and confined circumstellar material is ejected during the last episode of radial pulsation before the explosion. Notably, we find strong evidence for variations of $$\tau$$ or $$T_\text{eff}$$ along with luminosity, a necessary assumption to reproduce the wavelength-dependent variability, which implies periodic dust sublimation and condensation. Given the observed SED, partial dust obscuration remains possible, but any unobstructed binary companion over $$5.6\, \mathrm{ M}_\odot$$ can be ruled out. 

Abstract The Bright Transient Survey (BTS) aims to obtain a classification spectrum for all bright (m_peak≤ 18.5 mag) extragalactic transients found in the Zwicky Transient Facility (ZTF) public survey. BTS critically relies on visual inspection (“scanning”) to select targets for spectroscopic follow-up, which, while effective, has required a significant time investment over the past ∼5 yr of ZTF operations. We presentBTSbot, a multimodal convolutional neural network, which provides a bright transient score to individual ZTF detections using their image data and 25 extracted features.BTSbotis able to eliminate the need for daily human scanning by automatically identifying and requesting spectroscopic follow-up observations of new bright transient candidates.BTSbotrecovers all bright transients in our test split and performs on par with scanners in terms of identification speed (on average, ∼1 hr quicker than scanners). We also find thatBTSbotis not significantly impacted by any data shift by comparing performance across a concealed test split and a sample of very recent BTS candidates.BTSbothas been integrated intoFritzandKowalski, ZTF’s first-party marshal and alert broker, and now sends automatic spectroscopic follow-up requests for the new transients it identifies. Between 2023 December and 2024 May,BTSbotselected 609 sources in real time, 96% of which were real extragalactic transients. WithBTSbotand other automation tools, the BTS workflow has produced the first fully automatic end-to-end discovery and classification of a transient, representing a significant reduction in the human time needed to scan. 

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances has been challenging due to the computational cost. In this paper, we propose a persistence diagram hashing framework that learns a binary code representation of persistence diagrams, which allows for fast computation of distances. This framework is built upon a generative adversarial network (GAN) with a diagram distance loss function to steer the learning process. Instead of using standard representations, we hash diagrams into binary codes, which have natural advantages in large-scale tasks. The training of this model is domain-oblivious in that it can be computed purely from synthetic, randomly created diagrams. As a consequence, our proposed method is directly applicable to various datasets without the need for retraining the model. These binary codes, when compared using fast Hamming distance, better maintain topological similarity properties between datasets than other vectorized representations. To evaluate this method, we apply our framework to the problem of diagram clustering and we compare the quality and performance of our approach to the state-of-the-art. In addition, we show the scalability of our approach on a dataset with 10k persistence diagrams, which is not possible with current techniques. Moreover, our experimental results demonstrate that our method is significantly faster with the potential of less memory usage, while retaining comparable or better quality comparisons. 

The persistence diagram (PD) is an important tool in topological data analysis for encoding an abstract representation of the homology of a shape at different scales. Different vectorizations of PD summary are commonly used in machine learning applications, however distances between vectorized persistence summaries may differ greatly from the distances between the original PDs. Surprisingly, no research has been carried out in this area before. In this work we compare distances between PDs and between different commonly used vectorizations. Our results give new insights into comparing vectorized persistence summaries and can be used to design better feature-based learning models based on PDs