New ELM algorithms reduce computation time and complexity.
problem Efficient computation of extreme learning machine (ELM) algorithms.
method Developed inverse-free ELM algorithms using recursive matrix inverse and inverse LDL' factorization.
result Proposed algorithms significantly reduce computational complexity.
Paper reconstructs compact metric spaces using finite approximations and inverse persistence.
problem Reconstructing the homotopy type of compact metric spaces.
method Using inverse limit of finite approximations and inverse persistence.
result Definition of inverse persistence as a new persistence process.
Proof of convergence for multi-objective optimization using inverse reinforcement learning.
problem Proving convergence in multi-objective optimization problems.
method Wasserstein inverse reinforcement learning with projective subgradient method and gradient descent.
result Convergence of inverse reinforcement learning for multi-objective optimization.
Paper proves rigidity of inversive distance circle packings.
problem Proving rigidity of inversive distance circle packings.
method Variational principles and combinatorial curvature study.
result Global rigidity of inversive distance circle packings proved.
Two new inverse-free ELM algorithms for incremental and decremental learning are proposed.
problem Efficiently updating and removing multiple hidden nodes in ELM.
method Improved inverse-free recursive algorithms for Tikhonov regularization.
result Inverse-free algorithms for ELM with multiple hidden nodes and redundant nodes.
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…
New method for estimating parameters in inverse problems using double robustness.
problem Estimating parameters defined as linear functionals of solutions to linear inverse problems.
method Source condition double robust inference method that uses iterated Tikhonov regularized adversarial estimators.
result Asymptotic normality of the parameter of interest as long as either the primal or dual inverse problem is sufficiently well-posed.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
problem Invalidity of existing inverse theorems for mesh group-planes.
method Classification of three and five point meshes, analysis of joint invariant signatures.
result Valid conditions for the Signature-inverse Theorem in mesh group-planes.
Seismic inversion method uses GAN to improve efficiency and accuracy.
problem Difficulty in combining geological knowledge with seismic data and assessing uncertainty.
method Generative Adversarial Network (GAN) for seismic inversion.
result GAN-generated models conform to observation data with low uncertainty.
Easy condition for local k-connectedness in inverse limits of polyhedra.
problem Local k-connectedness of inverse limits of polyhedra.
method Easy condition for local k-connectedness.
result Provided an easily verifiable condition.
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
The paper studies Möbius inversion on surfaces in Minkowski 3-space.
problem Understanding transformations of surfaces in Minkowski space.
method Definition and properties of Möbius inversion on surfaces in Minkowski 3-space.
result Möbius inversion preserves lines of principal curvature and degenerate metric points but not parabolic sets.
CNN outperforms other methods in gravity inversion.
problem Estimating subsurface density from gravitational field data.
method CNN, VAEs, GANs, iterative solvers (GD, GMRES, LGMRES, ICG).
result CNN provides the most reliable reconstructions.
The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…
Paper proposes efficient image inversion and editing using rectified stochastic differential equations.
problem Inversion and editing of real images using generative models.
method Proposes RF inversion using dynamic optimal control and a linear quadratic regulator, extending to stochastic sampler for Flux.
result Allows state-of-the-art performance in zero-shot inversion and editing, outperforming prior works.
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…
Develops a method to interpolate data for efficient inversion in nonuniform geometries.
problem Efficient inversion in nonuniform geometries where not all sources see all receivers.
method Interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots.
result Illustrates the flexibility and efficiency of the approach using synthetic experiments.
Deep learning approach to inverse optimization.
problem Determine parameters of an optimization process from observations.
method Unroll iterative optimization, use backpropagation to learn parameters.
result Learn coefficients for cost vector and constraints in linear programs.
New filters improve radar target inference in complex scenarios.
problem Improving radar target inference in highly non-linear system models.
method Developed inverse cubature Kalman filter (I-CKF), inverse quadrature Kalman filter (I-QKF), and inverse cubature-quadrature Kalman filter (I-CQKF) for non-linear systems.
result Numerical experiments show improved estimation accuracy compared to existing methods.
Global inverse function theorem proved easily using Riemannian geometry.
problem Global inverse function theorem in Riemannian geometry.
method Hopf--Rinow theorem in Riemannian geometry.
result Hadamard's global inverse function theorem is proven easily.
Deep learning methods improve Bayesian inversion for efficient 3D imaging.
problem Efficiently solving large-scale inverse problems in medical imaging.
method Two novel deep learning approaches: WGAN with mini-discriminator and neural network loss function.
result Both methods compute posterior mean and standard deviation efficiently, demonstrating promising performance in 3D imaging.
Study uses machine learning to solve photoacoustic tomography's inverse problem.
problem Solving the full inverse problem in photoacoustic tomography.
method Developed an approach using variational autoencoders for Bayesian estimation of the posterior distribution.
result Evaluated the approach with numerical simulations and compared it to a Bayesian solution.
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
MCGDiff uses SGM to guide SMC for solving ill-posed linear inverse problems.
problem Solving ill-posed linear inverse problems in Bayesian settings.
method Exploiting SGM structure, defining a sequence of intermediate problems, and using SMC methods.
result MCGDiff outperforms competing methods in Bayesian ill-posed inverse problems.
Determinantal averaging corrects inversion bias in distributed Newton's method.
problem Inverting a sum of distributed matrices is biased; local averages are incorrect.
method Reweighting local estimates of the Newton's step proportionally to the determinant of the local Hessian estimate, then averaging them.
result Determinantal averaging provides the first known asymptotically consistent distributed Newton step.
Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.
problem Evolution of hypersurfaces in spacetime.
method Weak solutions for hypersurfaces evolving along inverse spacetime mean curvature in asymptotically flat maximal initial data sets.
result Weak solution detects both future- and past-trapped apparent horizons.
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
New inequalities for Steklov eigenvalues traced and inverted.
problem Steklov eigenvalues and their traces.
method Obtained new inequalities for Steklov eigenvalues.
result New inequalities for trace and inverse trace of Steklov eigenvalues.
Study on positivity in inverse σ-flow convergence for (n-1, n-1) cohomology classes.
problem Finding necessary and sufficient conditions for solvability of inverse σ_k equations.
method Analyzing positivity in the inverse σ_{n-1}-flow for (n-1, n-1) cohomology classes.
result Partial verification of conjecture for inverse σ_{n-1}-flow and 3-folds.
Two efficient ridge solutions improve BLS for new inputs, enhancing accuracy and speed.
problem Improving BLS for new added inputs in a learning system.
method Proposes recursive and square-root BLS algorithms using inverse and inverse Cholesky factor updates.
result Both proposed ridge solutions improve BLS accuracy and speed, especially with larger lambda.
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
problem Solving inverse eigenvalue problems for symmetric potentials and refractive indices.
method Supervised regression models (k-Nearest Neighbours, Random Forests, Multi-Layer Perceptron) trained on eigenvalue datasets.
result Machine learning methods can numerically solve inverse eigenvalue problems under appropriate parameter tuning.
Inverts operator on hyperbolic surfaces, constructing invariant distributions.
problem Constructing explicit inversion formula for X-ray normal operator.
method First, inversion formula for attenuated normal operator on Poincaré disk and closed hyperbolic surfaces. Then, explicit construction of invariant distributions.
result Explicit construction of invariant distributions with prescribed pushforward.
Abstract: Generalizes Milnor-Schwarz lemma to inverse monoids.
problem Applying Milnor-Schwarz lemma to inverse monoids.
method Two proofs provided: elementary and using Vietoris-Rips complex.
result Generalization of Milnor-Schwarz lemma to inverse monoids.
New constructions show non-rigidity in spherical inversive distance circle packings.
problem Non-rigidity of spherical inversive distance circle packings.
method Elementary constructions in inversive geometry of the 2-sphere.
result Show non-rigidity without using Euclidean polyhedra or Pogorelov maps.
Proves rigidity of circle packings in the plane, generalizing previous work.
problem Rigidity of infinite inversive distance circle packings in the plane.
method Maximal principle for generic weighted Delaunay inversive distance circle packings and ring lemma for inversive distance circle packings in hexagonal triangulated plane.
result Proves Bowers-Stephenson's conjecture for inversive distance circle packings.
A new neural network approach for inverse problems.
problem Solving inverse problems in medical imaging and computer vision.
method Using a neural network as a regularization functional to learn from unsupervised data.
result The proposed framework can be applied even with unsupervised training data.
EnKG solves inverse problems without derivatives, using diffusion models.
problem Solving inverse problems with derivative-free methods.
method Ensemble Kalman Diffusion Guidance (EnKG) using diffusion models.
result EnKG can solve inverse problems with only forward model evaluations.
Surveying inverse problems on manifolds with boundaries.
problem Inverse problems for geometric structures on manifolds with boundaries.
method Analyzes linear and non-linear geometric inverse problems.
result Recent results on geodesic X-ray transforms and Riemannian metrics.
Estimates joint inverse covariances with shared structure across groups.
problem Joint estimation of structured inverse covariance matrices.
method Optimization algorithm exploiting shared linear structure.
result Improves estimation of inverse covariances.
We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.
We solve image inverse problems using a flow-based noise model.
problem Image inverse problems with complex noise patterns.
method Normalizing flow prior for maximum a posteriori estimation.
result Empirical validation on various inverse problems.
Study on Frobenius manifold structures and inversion symmetry.
problem Understanding inversion symmetry in solutions to Witten-Dijkgraaf-Verlinde-Verlinde equations.
method Using conjugacy relations on Frobenius manifold structures and flat pencils of metrics.
result Geometric interpretation of inversion symmetry.
Paper shows how sparse inversion speeds up log determinant derivatives.
problem Deriving log determinant derivatives for sparse matrices.
method Sparse inversion, selected inversion, accelerates computation.
result Derivative of log determinant can be computed faster with sparse inversion.
Method estimates sparse inverse covariance and partial correlation matrices efficiently.
problem Sparse high-dimensional inverse covariance and partial correlation matrix estimation.
method Two-stage estimation method using partial regression with positive semi-definiteness.
result Efficient estimation of inverse covariance and partial correlation matrices with derived non-asymptotic rates.
Enhances OTA FL algorithms by defining inverse feasibility for linear models.
problem Improving security and privacy in over-the-air federated learning.
method Defines inverse feasibility as an upper bound on condition number, analyzes existing model, proposes new model.
result Proposes a new OTA FL model with enhanced characteristics.
Seismic inversion improved using semi-supervised sequence modeling.
problem Lack of geophysical constraints in machine learning seismic inversion.
method Semi-supervised sequence modeling with recurrent neural networks.
result Achieved 98% correlation between estimated and target elastic impedance.
Study solves inverse problems for real principal type operators using unique data sets and ray transforms.
problem Determining coefficients in real principal type equations from boundary data.
method Unique data sets, bicharacteristic ray transforms, and propagation of singularities.
result Global uniqueness results for determining coefficients in nonlinear real principal type equations.
We explore inverse and quanto inverse crypto options, their pricing, and applications.
problem Market incompleteness in crypto options trading.
method Comparison of direct and inverse options, and introduction of currency-protected 'quanto' options.
result Pricing and hedging characteristics of inverse and quanto inverse options in a Black-Scholes framework.