相关论文: Machine Learning Line Bundle Connections

A very popular model in machine learning is the feedforward neural network (FFN). The FFN can approximate general functions and mitigate the curse of dimensionality. Here we introduce FFNs which represent sections of holomorphic line…

We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…

We present a response-augmented machine learning (ML) approach to the energetics of electrified metal surfaces. We leverage local descriptors to learn the work function as the first-order energy change to introduced bias charges and…

In this note we introduce a Yang-Mills bar equation on complex vector bundles over compact Hermitian manifolds as the Euler-Lagrange equation for a Yang-Mills bar functional. We show the existence of a non-trivial solution of this equation…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

We exhibit a transformation taking special Lagrangian submanifolds of a Calabi-Yau together with local systems to vector bundles over the mirror manifold with connections obeying deformed Hermitian-Yang-Mills equations. That is, the…

Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific…

Modern statistical machine translation (SMT) systems usually use a linear combination of features to model the quality of each translation hypothesis. The linear combination assumes that all the features are in a linear relationship and…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…

Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…

Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated…

In this manuscript, we demonstrate, using several regression techniques, that the remaining independent Hodge numbers of complete intersection Calabi-Yau four-folds and five-folds can be machine learned from $h^{1,1}$ and $h^{2,1}$.…

Precise nanofabrication represents a critical challenge to developing semiconductor quantum-dot qubits for practical quantum computation. Here, we design and train a convolutional neural network to interpret in-line scanning electron…

We discuss a machine learning (ML) regression model to reduce the computational cost of disconnected diagrams in lattice QCD calculations. This method creates a mapping between the results of fermionic loops computed at different quark…

Free quotients of Calabi-Yau manifolds play an important role in string compactification. In this paper, we explore machine learning techniques, such as fully connected neural networks and multi-head attention (MHA) models, as a potential…

Accurate path loss (PL) prediction is crucial for successful network planning, antenna design, and performance optimization in wireless communication systems. Several conventional approaches for PL prediction have been adopted, but they…

In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We calculate the virtual dimension of the moduli space of HYM connections and provide an analytic proof…