Related papers: Discovery of Probabilistic Dirichlet-to-Neumann Ma…
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…
Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
In this paper we show uniqueness of the conductivity for the quasilinear Calder\'on's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary…
Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. This model selection problem can be challenging due to its large combinatorial search space, particularly when dealing with non-parametric…
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…
We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…
We study the asymptotic behavior of Dirichlet minimizers to the Allen--Cahn equation on manifolds with boundary, and we relate the Neumann data to the geometry of the boundary. We show that Dirichlet minimizers are asymptotically local in…
Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
We show that measurements of the Neumann-to-Dirichlet map, roughly speaking, on a certain part of the boundary of a smooth domain in dimension 3 or higher, for inputs with support restricted to the other part, determine an electric…
Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…