Related papers: Symbolic Graph Networks for Robust PDE Discovery f…
While robust graph neural networks (GNNs) have been widely studied for graph perturbation and attack, those for label noise have received significantly less attention. Most existing methods heavily rely on the label smoothness assumption to…
The discovery of partial differential equations (PDEs) from datasets has attracted increased attention. However, the discovery of governing equations from sparse data with high noise is still very challenging due to the difficulty of…
Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input…
Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…
In this article, we propose a sparse spectra graph convolutional network (SSGCNet) for solving Epileptic EEG signal classification problems. The aim is to achieve a lightweight deep learning model without losing model classification…
Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…
Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…
The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…
While Graph Neural Networks (GNNs) are powerful models for learning representations on graphs, most state-of-the-art models do not have significant accuracy gain beyond two to three layers. Deep GNNs fundamentally need to address: 1).…
Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs…
Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we…
We present a generic framework for spatio-temporal (ST) data modeling, analysis, and forecasting, with a special focus on data that is sparse in both space and time. Our multi-scaled framework is a seamless coupling of two major components:…
This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
Dynamic graph neural networks have been widely used in modeling and representation learning of graph structure data. Current dynamic representation learning focuses on either discrete learning which results in temporal information loss or…
This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current…