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The deep learning (DL) has been penetrating daily life in many domains, how to keep the DL model inference secure and sample privacy in an encrypted environment has become an urgent and increasingly important issue for various…

Cryptography and Security · Computer Science 2025-12-01 Wenbo Song , Xinxin Fan , Quanliang Jing , Shaoye Luo , Wenqi Wei , Chi Lin , Yunfeng Lu , Ling Liu

This letter proposes a novel deep learning framework (DLF) that addresses two major hurdles in the adoption of deep learning techniques for solving physics-based problems: 1) requirement of the large dataset for training the DL model, 2)…

Applied Physics · Physics 2021-10-25 Shivanshu Mishra , Bipin Gaikwad , Nidhi Chaturvedi

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Numerical Analysis · Mathematics 2025-07-30 Patrick Chatain , Michael Rizvi-Martel , Guillaume Rabusseau , Adam Oberman

Hyperspectral image (HSI) denoising is an essential procedure for HSI applications. Unfortunately, the existing Transformer-based methods mainly focus on non-local modeling, neglecting the importance of locality in image denoising.…

Image and Video Processing · Electrical Eng. & Systems 2024-08-05 Hao Liang , Chengjie , Kun Li , Xin Tian

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Numerical Analysis · Mathematics 2024-05-10 Yan Xie , Minrui Lv , Chensong Zhang

When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is the loss function to be minimised, which should ideally correspond to a norm of the error. In multiple problems, this error norm coincides…

Numerical Analysis · Mathematics 2022-10-26 Jamie M. Taylor , David Pardo , Ignacio Muga

Hybrid optical neural networks (HONNs) offload some electronic computation to optical preprocessors to achieve low-power and fast training and inference phases in machine learning tasks. Our contribution to the development of HONNs is a…

Optics · Physics 2025-10-07 Altai Perry , Luat Vuong

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…

Machine Learning · Computer Science 2024-01-22 Yiheng Du , Nithin Chalapathi , Aditi Krishnapriyan

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

Numerical Analysis · Mathematics 2025-12-11 Nils Margenberg , Carolin Mehlmann

In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…

Numerical Analysis · Mathematics 2024-10-11 Shukai Du , Samuel N. Stechmann

Learning-based single image super-resolution (SISR) methods are continuously showing superior effectiveness and efficiency over traditional model-based methods, largely due to the end-to-end training. However, different from model-based…

Image and Video Processing · Electrical Eng. & Systems 2020-03-24 Kai Zhang , Luc Van Gool , Radu Timofte

Index modulation (IM) brings the reduction of power consumption and complexity of the transmitter to classical multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. However, due to the introduction…

Signal Processing · Electrical Eng. & Systems 2019-11-14 Jinxue Liu , Hancheng Lu

This paper explores the problem of hyperspectral image (HSI) super-resolution that merges a low resolution HSI (LR-HSI) and a high resolution multispectral image (HR-MSI). The cross-modality distribution of the spatial and spectral…

Image and Video Processing · Electrical Eng. & Systems 2021-02-03 Zhiyu Zhu , Junhui Hou , Jie Chen , Huanqiang Zeng , Jiantao Zhou

Fully Homomorphic Encryption (FHE) allows for computation directly on encrypted data and enables privacy-preserving neural inference in the cloud. Prior work has focused on models with dense inputs (e.g., CNNs), with less attention given to…

Cryptography and Security · Computer Science 2026-02-23 Karthik Garimella , Austin Ebel , Gabrielle De Micheli , Brandon Reagen

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

Numerical Analysis · Mathematics 2024-09-05 Xiaodong Feng , Haojiong Shangguan , Tao Tang , Xiaoliang Wan , Tao Zhou

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…

Machine Learning · Computer Science 2026-03-20 Mominul Rubel , Adam Meyers , Gabriel Nicolosi

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Machine Learning · Computer Science 2025-01-09 Zijie Li , Saurabh Patil , Francis Ogoke , Dule Shu , Wilson Zhen , Michael Schneier , John R. Buchanan, , Amir Barati Farimani

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output)…

Signal Processing · Electrical Eng. & Systems 2022-01-04 Ahmet M. Elbir , Kumar Vijay Mishra , M. R. Bhavani Shankar , Björn Ottersten

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Numerical Analysis · Mathematics 2024-03-20 Janina E. Schütte , Martin Eigel

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Machine Learning · Computer Science 2024-09-10 Ye Li , Ting Du , Yiwen Pang , Zhongyi Huang