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We introduce a novel approach to the three-dimensional reconstruction of superfluid vortex filaments using deep convolutional neural networks. Superfluid vortices, quantum mechanical phenomena of immense scientific interest, are challenging…

Quantum Gases · Physics 2023-12-25 Nick Keepfer , Thomas Flynn , Nick Parker , Thomas Billam

A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…

Numerical Analysis · Mathematics 2017-02-01 Pia Domschke , Aseem Dua , Jeroen J. Stolwijk , Jens Lang , Volker Mehrmann

We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis. The learned representations enjoy Lipschitz stability with…

Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods…

Machine Learning · Computer Science 2026-01-05 Xinyang Chen , Amaël Broustet , Guanyuan Zeng , Cheng He , Guoting Chen

Across many scientific domains, practitioners rely on coarse, discretized summaries to track the evolving structure of complex systems under noise, measurement error, and changing system size. Understanding when such summaries are reliable…

Algebraic Topology · Mathematics 2026-01-29 Chad M. Topaz

Transformer-based models for time series forecasting (TSF) have attracted significant attention in recent years due to their effectiveness and versatility. However, these models often require extensive hyperparameter optimization (HPO) to…

Machine Learning · Computer Science 2025-01-03 Jingjing Xu , Caesar Wu , Yuan-Fang Li , Grégoire Danoy , Pascal Bouvry

Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…

Computational Geometry · Computer Science 2021-04-19 Samantha Chen , Yusu Wang

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…

Computational Engineering, Finance, and Science · Computer Science 2025-09-18 Aaron Lutheran , Srijan Das , Alireza Tabarraei

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

Algebraic Topology · Mathematics 2026-02-27 Pepijn Roos Hoefgeest , Lucas Slot

Medical tubular anatomical structures are inherently three-dimensional conduits with lumens, enclosing walls, and complex branching topologies. Accurate reconstruction of their geometry and topology is crucial for applications such as…

Computer Vision and Pattern Recognition · Computer Science 2026-03-26 Minghui Zhang , Yaoyu Liu , Junyang Wu , Xin You , Hanxiao Zhang , Junjun He , Yun Gu

Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…

Algebraic Topology · Mathematics 2024-06-26 Inés García-Redondo , Anthea Monod , Anna Song

A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…

Statistical Mechanics · Physics 2007-05-23 R. C. Venkatesan

This paper focuses on estimating probability distributions over the set of 3D rotations ($SO(3)$) using deep neural networks. Learning to regress models to the set of rotations is inherently difficult due to differences in topology between…

Computer Vision and Pattern Recognition · Computer Science 2020-06-18 D. Mohlin , G. Bianchi , J. Sullivan

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…

Computational Geometry · Computer Science 2019-03-25 Frédéric Chazal , Vincent Divol

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

Computer Vision and Pattern Recognition · Computer Science 2024-08-12 Lu Sang , Abhishek Saroha , Maolin Gao , Daniel Cremers

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…

Statistical Mechanics · Physics 2021-05-26 Quoc Hoan Tran , Mark Chen , Yoshihiko Hasegawa

Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three…

Quantum Physics · Physics 2023-03-08 Lorenzo M. Procopio

Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…

Computer Vision and Pattern Recognition · Computer Science 2012-05-17 Jason Chang , John W. Fisher

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…

Cosmology and Nongalactic Astrophysics · Physics 2021-12-15 Janis Fluri , Aurelien Lucchi , Tomasz Kacprzak , Alexandre Refregier , Thomas Hofmann

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

Machine Learning · Computer Science 2021-06-01 Michael Moor , Max Horn , Bastian Rieck , Karsten Borgwardt