Promising directions of machine learning for partial differential equations

SL Brunton, JN Kutz - Nature Computational Science, 2024 - nature.com
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

On the use of deep learning for computational imaging

G Barbastathis, A Ozcan, G Situ - Optica, 2019 - opg.optica.org
Since their inception in the 1930–1960s, the research disciplines of computational imaging
and machine learning have followed parallel tracks and, during the last two decades …

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

Z Long, Y Lu, B Dong - Journal of Computational Physics, 2019 - Elsevier
Partial differential equations (PDEs) are commonly derived based on empirical
observations. However, recent advances of technology enable us to collect and store …

Pde-net: Learning pdes from data

Z Long, Y Lu, X Ma, B Dong - International conference on …, 2018 - proceedings.mlr.press
Partial differential equations (PDEs) play a prominent role in many disciplines of science
and engineering. PDEs are commonly derived based on empirical observations. However …

Deep convolutional framelets: A general deep learning framework for inverse problems

JC Ye, Y Han, E Cha - SIAM Journal on Imaging Sciences, 2018 - SIAM
Recently, deep learning approaches with various network architectures have achieved
significant performance improvement over existing iterative reconstruction methods in …

Weighted low-rank tensor recovery for hyperspectral image restoration

Y Chang, L Yan, XL Zhao, H Fang… - IEEE transactions on …, 2020 - ieeexplore.ieee.org
Hyperspectral imaging, providing abundant spatial and spectral information simultaneously,
has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations …

Embedding hard physical constraints in neural network coarse-graining of 3D turbulence

AT Mohan, N Lubbers, D Livescu… - arxiv preprint arxiv …, 2020 - arxiv.org
In the recent years, deep learning approaches have shown much promise in modeling
complex systems in the physical sciences. A major challenge in deep learning of PDEs is …

[HTML][HTML] Data-driven tight frame construction and image denoising

JF Cai, H Ji, Z Shen, GB Ye - Applied and Computational Harmonic …, 2014 - Elsevier
Sparsity-based regularization methods for image restoration assume that the underlying
image has a good sparse approximation under a certain system. Such a system can be a …

[HTML][HTML] Applications of machine vision in pharmaceutical technology: A review

DL Galata, LA Meszaros, N Kallai-Szabo… - European Journal of …, 2021 - Elsevier
The goal of this paper is to give an introduction to analysis of images acquired by a digital
camera with visible illumination and to review its applications as a Process Analytical …

Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging

Y Liu, Z Zhan, JF Cai, D Guo, Z Chen… - IEEE transactions on …, 2016 - ieeexplore.ieee.org
Compressed sensing (CS) has exhibited great potential for accelerating magnetic
resonance imaging (MRI). In CS-MRI, we want to reconstruct a high-quality image from very …