arXiv research

PINN-FEM combines PINNs and FEM for accurate Dirichlet boundary condition enforcement.

Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.

A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within an image to simultaneously estimate boundaries for objects within images with mo…

Abstract: Determines thermoelastic coefficients from boundary data.

New BdryMatérn GP model for reliable boundary integration on irregular domains.

Stokes' theorem's boundary maximizes entropy.

Many recent works on knowledge distillation have provided ways to transfer the knowledge of a trained network for improving the learning process of a new one, but finding a good technique for knowledge distillation is still an open problem. In this paper, we provide a new perspective based on a decision boundary, which…

Uniform K-homology theory applied to elliptic operators on manifolds with boundary.

Proposes neural networks for solving complex free boundary problems.

Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.

We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of the area and the height in terms of the boundary. In case that the boundary is a …

Physics-informed neural networks improve by measuring effective dimensionality of constraints.

Stable actions of hyperbolic groups on their boundaries.

New method uses entropy dissipation to prove isoperimetric inequalities.

We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations for the components of a compactification of the given metric. This…

Researchers derive asymptotic expansions for thermoelastic operators on manifolds.

Enhances neural network solvers for PDEs with complex boundary conditions.

Study reveals how to determine area and curvature from fluid flow resonances.

We show that reinforcement learning agents that learn by surprise (surprisal) get stuck at abrupt environmental transition boundaries because these transitions are difficult to learn. We propose a counter-intuitive solution that we call Mutual Information Minimising Exploration (MIME) where an agent learns a latent rep…

Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results…

We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the boundary. We show that one can recover uniquely and in a stable way a conformal factor …

Positive curvature forces foliation leaf spaces to have boundaries.

For a compact Riemannian manifold with boundary, we want to find the metric structure from knowledge of distances between boundary points. This is called the "boundary rigidity problem". If the boundary is not concave, which means locally not all shortest paths lie entirely in the boundary, then we are able to find the…

D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels methods for boundary conditions of Dirichlet and Von Neumann type. Moreover we consi…

Revisits information metric as pseudo metric on observables, with applications to conditional independence.

Physics-informed methods infer spatial dynamics from static snapshots, but limits exist.

The paper explores geometry of probability measures and barycenter maps.

For a given bounded domain $Ω\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as $t\to 0^+$. These coefficients (i.e., heat invariants) provide precise information for the volume of the domain $…

Bayesian PINNs learn elliptic PDEs with near-minimax posterior contraction rate.

Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is stated which implies uniqueness and stability for this problem. If the conformal c…

A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.

In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for word hyperbolic groups, where it was well-known that each such group admitted a unique boundary---in a very stong sense. Prior to Croke and Kleiner's discovery, it had been observed by Geoghe…

We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1- α$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the statistical accuracies and computational efficiency of these algorithms depend on the degr…

Study on curvature functions for compact manifolds with boundary.

Algorithm learns Bayesian network structure efficiently from data.

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the c…

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 loca…

BEKAN uses RBFs and evolutionary methods to solve PDEs with boundary conditions.

For a bounded domain $Ω\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the trace of the strongly continuous semigroup associated with the Navier-Lamé operator on $Ω$ as $t\to 0^+$. These coefficients (i.e., spectral invariants) provide precise …

Sharp generalization of boundary regularity for area minimizing currents with arbitrary multiplicity.

Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.

Kernel-based GPs model continuous processes with uncountable information.

New model of vague knowledge without strict partitions or transitivity.

We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which ha…

Proposes a boundary detection method inspired by LLE for high-dimensional data.

New DDMs use neural networks for solving equations on manifold shapes.

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still rema…

The goal of a decision-based adversarial attack on a trained model is to generate adversarial examples based solely on observing output labels returned by the targeted model. We develop HopSkipJumpAttack, a family of algorithms based on a novel estimate of the gradient direction using binary information at the decision…