Related papers: Manifolds.jl: An Extensible Julia Framework for Da…
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
Despite the popularity of the manifold hypothesis, current manifold-learning methods do not support machine learning directly on the latent $d$-dimensional data manifold, as they primarily aim to perform dimensionality reduction into…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
Co-developing scientific algorithms and hardware accelerators requires domain-specific knowledge and large engineering resources. This leads to a slow development pace and high project complexity, which creates a barrier to entry that is…
We present FreeBird, an extensible Julia-based platform for computational studies of phase equilibria at generic interfaces. The package supports a range of system configurations, from atomistic solid surfaces to coarse-grained…
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…
Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular,…
In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features…
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and…
We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…
Machine learning is driving development across many fields in science and engineering. A simple and efficient programming language could accelerate applications of machine learning in various fields. Currently, the programming languages…
Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…
We introduce the third major version of Metatheory.jl, a Julia library for general-purpose metaprogramming and symbolic computation. Metatheory.jl provides a flexible and performant implementation of e-graphs and Equality Saturation (EqSat)…
In emerging scientific computing environments, matrix computations of increasing size and complexity are increasingly becoming prevalent. However, contemporary matrix language implementations are insufficient in their support for efficient…
A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…
FeAmGen.jl is a Julia package designed to generate Feynman diagrams and their corresponding amplitudes for various processes in particle physics. Utilizing the models in the Universal Feynman Output (UFO) format and Qgraf for diagram…
IntrinsicTimescales.jl is a Julia package to perform estimation of intrinsic neural timescales (INTs). INTs are defined as the time window in which prior information from an ongoing stimulus can affect the processing of newly arriving…
Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…
We present JDLL, an agile Java library that offers a comprehensive toolset/API to unify the development of high-end applications of DL for bioimage analysis and to streamline their installation and maintenance. JDLL provides all the…