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Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic…

Computer Vision and Pattern Recognition · Computer Science 2022-03-24 Lukas Koestler , Daniel Grittner , Michael Moeller , Daniel Cremers , Zorah Lähner

Spectral lines from interstellar molecules provide crucial insights into the physical and chemical conditions of the interstellar medium. Traditional spectral line analysis relies heavily on manual intervention, which becomes impractical…

Astrophysics of Galaxies · Physics 2026-01-14 Yisheng Qiu , Tianwei Zhang , Tie Liu , Fengyao Zhu , Dezhao Meng , Huaxi Chen , Thomas Möller , Peter Schilke , Donghui Quan

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Machine Learning · Computer Science 2026-04-03 Laurens R. Lueg , Victor Alves , Daniel Schicksnus , John R. Kitchin , Carl D. Laird , Lorenz T. Biegler

We consider deep learning strategies in ultrasound systems, from the front-end to advanced applications. Our goal is to provide the reader with a broad understanding of the possible impact of deep learning methodologies on many aspects of…

Signal Processing · Electrical Eng. & Systems 2019-07-30 Ruud JG van Sloun , Regev Cohen , Yonina C Eldar

Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…

Image and Video Processing · Electrical Eng. & Systems 2024-03-21 Ruiqing Sun , Delong Yang , Shaohui Zhang , Qun Hao

This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…

Mathematical Physics · Physics 2015-12-02 Mikhail Kudryavtsev , Sergio Palafox , Luis O. Silva

Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to…

Machine Learning · Computer Science 2016-08-05 Arvind Neelakantan , Quoc V. Le , Ilya Sutskever

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current…

Machine Learning · Computer Science 2019-11-11 Vardaan Pahuja , Jie Fu , Sarath Chandar , Christopher J. Pal

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

Numerical Analysis · Mathematics 2018-03-01 Hao Tian , Jing Zhang

Deep neural networks have rightfully won the place of one of the most accurate analysis tools in high energy physics. In this paper we will cover several methods of improving the performance of a deep neural network in a classification task…

Data Analysis, Statistics and Probability · Physics 2021-09-20 Lev Dudko , Petr Volkov , Georgii Vorotnikov , Andrei Zaborenko

Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the…

Solar and Stellar Astrophysics · Physics 2020-12-16 Ivan Milic , Ricardo Gafeira

We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…

Mathematical Physics · Physics 2008-11-26 P. Pedram , M. Mirzaei , S. S. Gousheh

Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep…

Machine Learning · Computer Science 2026-01-09 Georgios Is. Detorakis

Deep learning, in general, focuses on training a neural network from large labeled datasets. Yet, in many cases there is value in training a network just from the input at hand. This is particularly relevant in many signal and image…

Machine Learning · Computer Science 2024-04-09 Tom Tirer , Raja Giryes , Se Young Chun , Yonina C. Eldar

Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…

Machine Learning · Computer Science 2026-05-05 Michael F. Staddon

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…

Machine Learning · Computer Science 2016-02-22 Yong Ren , Yining Wang , Jun Zhu

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…

Artificial Intelligence · Computer Science 2026-03-20 Hongjue Zhao , Yizhuo Chen , Yuchen Wang , Hairong Qi , Lui Sha , Tarek Abdelzaher , Huajie Shao

Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…

Numerical Analysis · Mathematics 2023-10-11 Haifeng Zou , Xiaowen Xu , Chen-Song Zhang

Machine learning plays a role in many aspects of modern IR systems, and deep learning is applied in all of them. The fast pace of modern-day research has given rise to many approaches to many IR problems. The amount of information available…

Information Retrieval · Computer Science 2018-01-09 Tom Kenter , Alexey Borisov , Christophe Van Gysel , Mostafa Dehghani , Maarten de Rijke , Bhaskar Mitra

We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

Numerical Analysis · Mathematics 2024-04-15 Zhaodong Xu , Zhiqiang Sheng