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We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with…

Computer Vision and Pattern Recognition · Computer Science 2019-06-06 Hemant Kumar Aggarwal , Merry P. Mani , Mathews Jacob

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…

Dynamical Systems · Mathematics 2019-01-17 Samuel E. Otto , Clarence W. Rowley

This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…

Machine Learning · Computer Science 2023-03-22 A. Mavi , A. C. Bekar , E. Haghighat , E. Madenci

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Numerical Analysis · Mathematics 2021-04-21 Cheng Chang , Liu Liu , Tieyong Zeng

In this article, we propose a model-driven deep learning (DL) approach that combines DL with the expert knowledge to replace the existing orthogonal frequency-division multiplexing (OFDM) receiver in wireless communications. Different from…

Signal Processing · Electrical Eng. & Systems 2018-10-23 Xuanxuan Gao , Shi Jin , Chao-Kai Wen , Geoffrey Ye Li

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Machine Learning · Computer Science 2025-03-11 Viggo Moro , Luiz F. O. Chamon

In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…

Numerical Analysis · Mathematics 2025-08-06 Bo Yang , Xingquan Li , Jie Zhao , Ying Jiang

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Machine Learning · Computer Science 2021-09-14 Hao Xu , Dongxiao Zhang , Nanzhe Wang

We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset…

Numerical Analysis · Mathematics 2023-01-31 Massimiliano Lupo Pasini , Luka Malenica , Kwitae Chong , Stuart Slattery

Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…

Robotics · Computer Science 2023-08-25 Huu-Thiet Nguyen , Chien Chern Cheah , Kar-Ann Toh

The success of deep learning (DL) is often achieved with large models and high complexity during both training and post-training inferences, hindering training in resource-limited settings. To alleviate these issues, this paper introduces a…

Machine Learning · Computer Science 2025-01-20 En-hui Yang , Shayan Mohajer Hamidi

Partial differential equations (PDEs) are widely used for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or the solution of the…

Numerical Analysis · Mathematics 2025-10-17 Martina Bukač , Iva Manojlović , Boris Muha , Domagoj Vlah

To successfully apply trained neural network models to new domains, powerful transfer learning solutions are essential. We propose to introduce a novel cross-domain latent modulation mechanism to a variational autoencoder framework so as to…

Machine Learning · Computer Science 2024-02-01 Jinyong Hou , Jeremiah D. Deng , Stephen Cranefield , Xuejie Din

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Machine Learning · Statistics 2025-01-13 Noga Mudrik , Yenho Chen , Eva Yezerets , Christopher J. Rozell , Adam S. Charles

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Machine Learning · Computer Science 2025-02-14 Alessandro Longhi , Danny Lathouwers , Zoltán Perkó

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Numerical Analysis · Mathematics 2024-12-02 Nicola Farenga , Stefania Fresca , Simone Brivio , Andrea Manzoni

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Numerical Analysis · Mathematics 2022-01-11 Yihao Hu , Tong Zhao , Shixin Xu , Zhiliang Xu , Lizhen Lin

A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a…

Machine Learning · Statistics 2020-02-25 Guowei Zhang , Tao Ren , Yifan Yang

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

Machine Learning · Computer Science 2024-01-17 Xin-Yang Liu , Min Zhu , Lu Lu , Hao Sun , Jian-Xun Wang