Related papers: Uncertainty Modeling in Graph Neural Networks via …

The smoothing issue in graph learning leads to indistinguishable node representations, posing significant challenges for graph-related tasks. However, our experiments reveal that this problem can uncover underlying properties of node…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Graph Neural Networks (GNNs) are versatile, powerful machine learning methods that enable graph structure and feature representation learning, and have applications across many domains. For applications critically requiring interpretation,…

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or…

This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent…

In this work, we propose GLUE (Graph Deviation Network with Local Uncertainty Estimation), building on the recently proposed Graph Deviation Network (GDN). GLUE not only automatically learns complex dependencies between variables and uses…

Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…

Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering,…

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…

Continuous graph neural networks (CGNNs) have garnered significant attention due to their ability to generalize existing discrete graph neural networks (GNNs) by introducing continuous dynamics. They typically draw inspiration from…

Graph neural networks (GNNs) are powerful tools on graph data. However, their predictions are mis-calibrated and lack interpretability, limiting their adoption in critical applications. To address this issue, we propose a new…

Learning to compare two objects are essential in applications, such as digital forensics, face recognition, and brain network analysis, especially when labeled data is scarce and imbalanced. As these applications make high-stake decisions…

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…

The partial differential equation (PDE) plays a significantly important role in many fields of science and engineering. The conventional case of the derivation of PDE mainly relies on first principles and empirical observation. However, the…

Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or…

This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes…

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…