Related papers: Nested Head-Tail Vlasov Solver
This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed…
As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…
Terahertz (THz) imaging is one of the hotspots in the field of optics, where the depth information retrieval is a key factor to restore the three-dimensional appearance of objects. Impressive results for depth extraction in visible and…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an…
Training strategies for modern deep neural networks (NNs) tend to induce a heavy-tailed (HT) empirical spectral density (ESD) in the layer weights. While previous efforts have shown that the HT phenomenon correlates with good generalization…
Nanomagnets driven by spin currents provide a natural implementation for a neuron and a synapse: currents allow convenient summation of multiple inputs, while the magnet provides the threshold function. The objective of this paper is to…
We construct exact eigenvectors and eigenvalues for $U_q(\mathfrak{sp}_{2n})$- and $U_q(\mathfrak{so}_{2n})$-symmetric closed spin chains by means of a nested algebraic Bethe ansatz method. We use a fusion procedure to construct…
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
Nested Cavity Classifier (NCC) is a classification rule that pursues partitioning the feature space, in parallel coordinates, into convex hulls to build decision regions. It is claimed in some literatures that this geometric-based…
We investigate the solution landscape of a reduced Landau--de Gennes model for nematic liquid crystals on a two-dimensional hexagon at a fixed temperature, as a function of $\lambda$---the edge length. This is a generic example for reduced…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of…
The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…
A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced…
Machine learning (ML) is shaping our exploration of topological matter, whose existence is inherently tied to the geometry of quantum states or energy spectra. In non-Hermitian systems, distinctive spectral geometry can lead to topological…
The encoder-decoder is the typical framework for Neural Machine Translation (NMT), and different structures have been developed for improving the translation performance. Transformer is one of the most promising structures, which can…
We present here Nested_fit, a Bayesian data analysis code developed for investigations of atomic spectra and other physical data. It is based on the nested sampling algorithm with the implementation of an upgraded lawn mower robot method…