Neural networks are increasingly being used to solve partial differential equations (PDEs),
replacing slower numerical solvers. However, a critical issue is that neural PDE solvers …

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding
random noise is approximately equivalent to orthogonal perturbation. Hence, learning to …

We introduce a method for approximating the signed distance function (SDF) of geometry
corrupted by holes, noise, or self-intersections. The method implicitly defines a completed …

We introduce a data-driven version of the plus Cartan connection on the homogeneous
space M 2 of 2D positions and orientations. We formulate a theorem that describes all …

This paper proposes a deep-learning-based method for recovering a signed distance
function (SDF) of a given hypersurface represented by an implicit level set function. Using …

We propose a learning paradigm for numerical approximation of differential invariants of
planar curves. Deep neural-networks'(DNNs) universal approximation properties are utilized …

We introduce a new chamfering paradigm, locally connecting pixels to produce path
distances that approximate Euclidean space by building a small network (a replacement …

Neural networks, especially the recent proposed neural operator models, are increasingly
being used to find the solution operator of differential equations. Compared to traditional …

Terahertz tomographic imaging as well as machine learning tasks represent two emerging
fields in the area of nondestructive testing. Detecting outliers in measurements that are …

The approximation of both geodesic distances and shortest paths on point cloud sampled
from an embedded submanifold $\mathcal {M} $ of Euclidean space has been a long …