Related papers: Graph-based Prior and Forward Models for Inverse P…

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A…

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…

Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…

We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

Physics-informed neural networks (PINNs) have successfully addressed various computational physics problems based on partial differential equations (PDEs). However, while tackling issues related to irregularities like singularities and…

We propose a framework to study local gauge theories on manifolds with boundaries and asymptotic symmetries, which is based on representing them as so-called gauge PDEs. These objects extend the conventional BV-AKSZ sigma-models to the case…

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…