Related papers: Harnessing Scale and Physics: A Multi-Graph Neural…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…