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Geometric transformations have been widely used to augment the size of training images. Existing methods often assume a unimodal distribution of the underlying transformations between images, which limits their power when data with…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Tonmoy Hossain , Miaomiao Zhang

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

Numerical Analysis · Mathematics 2025-01-28 Zhanhong Ye , Xiang Huang , Leheng Chen , Hongsheng Liu , Zidong Wang , Bin Dong

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Numerical Analysis · Mathematics 2021-06-15 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly…

Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their…

Machine Learning · Computer Science 2025-01-23 Moshe Eliasof , Alessio Gravina , Andrea Ceni , Claudio Gallicchio , Davide Bacciu , Carola-Bibiane Schönlieb

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

Numerical Analysis · Mathematics 2023-03-22 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the…

Machine Learning · Computer Science 2024-10-16 Aoming Liang , Zhaoyang Mu , Pengxiao Lin , Cong Wang , Mingming Ge , Ling Shao , Dixia Fan , Hao Tang

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

Computational Engineering, Finance, and Science · Computer Science 2024-02-15 Roberto Perera , Vinamra Agrawal

Accurate, interpretable, and real-time modeling of multi-body dynamical systems is essential for predicting behaviors and inferring physical properties in natural and engineered environments. Traditional physics-based models face…

Machine Learning · Computer Science 2025-09-24 Vinay Sharma , Olga Fink

Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of…

Machine Learning · Computer Science 2024-06-28 Yifei Yang , Peng Wang , Xiaofan He , Dongmian Zou

In data systems, activities or events are continuously collected in the field to trace their proper executions. Logging, which means recording sequences of events, can be used for analyzing system failures and malfunctions, and identifying…

Machine Learning · Computer Science 2021-06-29 Tomer Meirman , Roni Stern , Gilad Katz

Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…

Data Structures and Algorithms · Computer Science 2021-05-06 Lars Gottesbüren , Tobias Heuer , Peter Sanders , Christian Schulz , Daniel Seemaier

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…

Computer Vision and Pattern Recognition · Computer Science 2025-12-30 Salvador Rodriguez-Sanz , Monica Hernandez

In the trend of hybrid Artificial Intelligence techniques, Physical-Informed Machine Learning has seen a growing interest. It operates mainly by imposing data, learning, or architecture bias with simulation data, Partial Differential…

Machine Learning · Computer Science 2024-08-05 Alexis-Raja Brachet , Pierre-Yves Richard , Céline Hudelot

Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work…

Machine Learning · Computer Science 2024-01-15 Bozhen Hu , Zelin Zang , Jun Xia , Lirong Wu , Cheng Tan , Stan Z. Li

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

Optimization and Control · Mathematics 2025-05-19 Ferdinand Vanmaele , Yara Elshiaty , Stefania Petra

Dementia disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD) exhibit overlapping electrophysiological signatures in EEG that challenge accurate diagnosis. Existing EEG-based methods are limited by full-band…

Machine Learning · Computer Science 2025-10-15 Jun-En Ding , Anna Zilverstand , Shihao Yang , Albert Chih-Chieh Yang , Feng Liu

Anomaly detection in high-dimensional time series data is pivotal for numerous industrial applications. Recent advances in multivariate time series anomaly detection (TSAD) have increasingly leveraged graph structures to model…

Machine Learning · Computer Science 2025-09-23 Jiazhen Chen , Mingbin Feng , Tony S. Wirjanto

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…

Machine Learning · Computer Science 2026-02-18 Siying Ma , Mehrdad M. Zadeh , Mauricio Soroco , Wuyang Chen , Jiguo Cao , Vijay Ganesh

As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing inferences with properties essential for physical realizability.…

Numerical Analysis · Mathematics 2020-12-23 Nathaniel Trask , Andy Huang , Xiaozhe Hu