Related papers: Discovery of Probabilistic Dirichlet-to-Neumann Ma…
We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…
We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…
Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…
Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from…
We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data"…
In this paper we study the Dirichlet-to-Neumann map for solutions to mean value formulas on trees. We give two alternative definition of the Dirichlet-to-Neumann map. For the first definition (that involves the product of a "gradient" with…
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…
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…
The problem of identifying the set of Dirichlet-to-Neumann (DtN) maps arising from conductivities on a smooth domain, among operators acting on functions on the boundary, is a challenging issue in the mathematical analysis of the Calder\'on…
Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$.…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calder\'on's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth bounded domain…
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…