相关论文: Rethinking the ill-posedness of the spectral funct…

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in many-body physics. However, the inversion is proved to be ill-posed in the realistic systems with noisy Green's functions. In this Letter,…

Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to…

The goal of Specular Neutron and X-ray Reflectometry is to infer materials Scattering Length Density (SLD) profiles from experimental reflectivity curves. This paper focuses on investigating an original approach to the ill-posed…

We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which…

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…

Recent studies suggest that artificial neural networks (ANNs) that match the spectral properties of the mammalian visual cortex -- namely, the $\sim 1/n$ eigenspectrum of the covariance matrix of neural activities -- achieve higher object…

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed…

Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different…

Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial,…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image recon-…

A general problem in quantum mechanics is the reconstruction of eigenstate wave functions from measured data. In the case of molecular aggregates, information about excitonic eigenstates is vitally important to understand their optical and…

In real-world applications with large state and action spaces, reinforcement learning (RL) typically employs function approximations to represent core components like the policies, value functions, and dynamics models. Although powerful…

An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…

Deep learning in k-space has demonstrated great potential for image reconstruction from undersampled k-space data in fast magnetic resonance imaging (MRI). However, existing deep learning-based image reconstruction methods typically apply…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

We propose a numerical spectral reconstruction workflow for high-temperature gauge theories that incorporates elements of semi-classical real-time evolution directly into standard lattice QCD simulations via high-temperature dimensional…

Hyperspectral image (HSI) super-resolution without additional auxiliary image remains a constant challenge due to its high-dimensional spectral patterns, where learning an effective spatial and spectral representation is a fundamental…

Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform…

Coherent imaging systems like synthetic aperture radar are susceptible to multiplicative noise that makes applications like automatic target recognition challenging. In this paper, NeighCNN, a deep learning-based speckle reduction algorithm…