arXiv research

Inverts operator on hyperbolic surfaces, constructing invariant distributions.

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including thos…

TgAE constructs surrogates for inverse modeling with theory-guided training.

Proves higher regularity for anisotropic inverse mean curvature flow.

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäck…

The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on…

Bayesian inverse problems solved with Gaussian models for PDEs.

Method constructs spirals with given tangents and curvatures.

Deep learning methods improve subsurface flow modeling efficiency.

Efficiently solves inverse problems with diffusion and flow models in just a few steps.

Constructs hyperspheres with prescribed mean curvature in Euclidean space.

The paper characterizes pedal curves of quadratic curves.

We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary …

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purp…

Develops trace class operators and inverse Laplacian theory for infinite dimensions.

The paper constructs a multi-valued inverse of quasiregular maps and develops pull-back theory for differential forms.

The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify differ…

We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing…

Researchers find counterexamples to inverse problems for wave equations.

With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is constructed from a solution of the field equation on the base manifold.

We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connecti…

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose--type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow …

This study proposes an efficient surrogate for Darcy flow inverse problems.

Researchers use GANs to infer physics-based inverse problems, quantifying uncertainty and promoting generalizability.

The article completes the research of two-point G$^2$ Hermite interpolation problem with spirals by inversion of conics. A simple algorithm is proposed to construct a family of 4th degree rational spirals, matching given G$^2$ Hermite data. A possibility to reduce the degree to cubic is discussed.

New method uses deep learning to solve inverse problems with provable guarantees.

In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the fundamental group of M in SL_{n+1}(R). The boundary is the inverse limit of an inve…

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a c…

Constructs a support-preserving homotopy for differential forms with boundary decay estimates.

We introduce a new geometric evolution equation for hypersurfaces in asymptotically flat spacetime initial data sets, that unites the theory of marginally outer trapped surfaces (MOTS) with the study of inverse mean curvature flow in asymptotically flat Riemannian manifolds. A theory of weak solutions is developed usin…

We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for bac…

New method solves blind inverse problems by optimizing both operator and image parameters.

Solves Apollonius' problem using oriented circles and inversive geometry.

We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of quantum fields in this space can be formulated as the inverse Radon transform, general…

New method uses Gaussian ODE filtering to approximate likelihoods for fast ODE inverse problems.

RADIS uses deep regression to create efficient importance sampling for model inversion and emulation.

New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.

New nonparametric estimators improve causal effect estimation.

We construct sequences of pseudo-Anosov mapping classes whose dilatations behave asymptotically like the inverse of the Euler characteristic of the surface they are defined on. These sequences are used to show that if the genus, g, and punctures, n, of a surface are related by a rational ray g=rn then the minimal dilat…

A new method maps high-dimensional Bayesian inverse problems to lower dimensions.

We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, existing var…

New method solves high-dimensional Bayesian inverse problems efficiently.

New methods for $Z$-transform inversion and Wiener-Hopf factorization.

In this paper we define the $p$-adic framed braid group ${\mathcal F}_{\infty,n}$, arising as the inverse limit of the modular framed braids and we give topological generators for ${\mathcal F}_{\infty, n}$. We also give geometric interpretations for the $p$-adic framed braids. We then construct a $p$-adic Yokonuma-Hec…

Adaptive operator learning reduces costs in Bayesian inverse problems.

The paper constructs metrics on spheres with families of minimal hypersurfaces.

This paper sets a lower bound for sample complexity in inverse reinforcement learning.