Study solves inverse problems for equations with fractional nonlinearities.
problem Solving inverse problems for semilinear elliptic equations with fractional power nonlinearities.
method Higher order linearization method adapted for fractional order.
result Results of previous studies remain valid for general power nonlinearities.
Proves solvability of general inverse σ_k equations with constant coefficients.
problem Solvability of general inverse σ_k equations with constant coefficients.
method Proves existence of unique solution if a C-subsolution exists.
result Confirms analytical conjecture for deformed Hermitian--Yang--Mills equation.
Solves inverse problem for Maxwell equations using vector fields.
problem Inverse problem for Maxwell equations in vacuum.
method Abstract theory of implicit differential equations over pre-symplectic manifolds.
result Provides solution for Maxwell equations using vector fields.
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.
Proves convexity of level sets of general inverse σ_k equations.
problem Convexity of level sets of general inverse σ_k equations.
method Analyzes level sets of degree n general inverse σ_k equations and uses numerical conditions to verify convexity.
result Proves convexity of level sets of general inverse σ_k equations.
Study inverse boundary value problem for Monge-Ampère equation on convex domains.
problem Determine a positive source function from the Dirichlet-to-Neumann map for Monge-Ampère equation.
method Recover Hessian as Riemannian metric, prove DN map uniqueness, develop asymptotic expansions, solve nonlocal ∂-equation. result DN map uniquely determines positive source function in convex Euclidean plane domains.
New criterion for solving inverse Hessian equations, including J-equation.
problem Existence of solutions to inverse Hessian equations, including J-equation.
method Stability of pairs in the sense of Paul, formulated in terms of GIT criterion.
result New numerical criterion for existence of solutions to inverse Hessian equations.
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 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.
Researchers find counterexamples to inverse problems for wave equations.
problem Inverse problems for wave equations on domains and Lorentzian manifolds.
method Constructing non-isometric Lorentzian metrics leading to same partial data measurements.
result Non-isometric Lorentzian metrics can produce identical partial data measurements.
Efficiently solves inverse PDE problems with Gaussian processes.
problem Solving inverse problems in linear PDEs with noisy data.
method Gaussian process regression with algebraic priors.
result High accuracy and computational efficiency achieved.
Inverse problem solved for relativistic Boltzmann equation on spacetime.
problem Determining spacetime from causal measurements.
method Using the nonlinearity of the Boltzmann equation to uniquely determine the spacetime.
result The spacetime is uniquely determined up to isometry in the causal set I+(x−)∩I−(x+). We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not…
The paper explores continuous inverse ambiguous functions on various Lie groups.
problem Existence of continuous inverse ambiguous functions on Lie groups.
method Investigation of continuous inverse ambiguous functions on specific Lie groups.
result Existence of continuous inverse ambiguous functions on various Lie groups.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Researchers solve an inverse problem for a semilinear elliptic equation on complex manifolds.
problem Determining an unknown function in a semilinear elliptic equation on complex manifolds.
method Analyzing higher order linearizations and interactions of Gaussian quasimode solutions.
result An unknown smooth function can be uniquely determined from the Dirichlet-to-Neumann map.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determinat…
New method finds precise late-time behavior of wave equations.
problem Analyzing late-time behavior of wave equations with inverse-square potentials.
method Physical-space-based method for deriving late-time asymptotics.
result Sharp, uniform decay estimates in time for asymptotic late-time tails.
In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…
The paper classifies shapes of translating solitons for a specific flow.
problem Understanding the shapes of translating solitons in a specific flow.
method Analyzing functions on a unit sphere and solving an ODE.
result Classification of the shapes of translating solitons.
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and sufficient algebraic and differential conditions for the existence of a variational…
This study proposes an efficient surrogate for Darcy flow inverse problems.
problem Efficiently constructing accurate surrogate models for high-dimensional complex inverse problems.
method Sequential Bayesian design strategy to acquire a locally accurate surrogate model focusing on high-probability regions.
result The proposed method accelerates inversion accuracy and computational speed.
This paper is an expository account of the development of soliton mathematics, from its inception in famous numerical experiments of Fermi-Pasta-Ulam and Zabusky-Kruskal to the recent synthesis of Terng-Uhlenbeck (dg-ga/9707004) that explains hidden symmetries of soliton equations in terms of loop-groups acting by dres…
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
problem Recover stiffness tensor and density from Dirichlet-to-Neumann map.
method Analyze invariance under coordinate transformations and gauge freedoms.
result Present gauge freedoms in the Dirichlet-to-Neumann map for Riemannian elastic wave equation.
We study two inverse problems on a globally hyperbolic Lorentzian manifold (M,g). The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood V⊂M of a time-like geodesic μ. Under natural causality conditions, we reconstruct the conformal type of the unknown open, relativ…
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, and the tau functions of the hierarchies are related by a Legendre type transformation. We also consider relationships b…
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 uses PINNs to solve complex PDEs with sparse measurements.
problem Joint estimation of source and parameters in advection-diffusion equations with limited data.
method Weighted adaptive approach based on neural tangent kernel of PINNs.
result Successful estimation of source function, velocity, and diffusion parameters.
We introduce and study generalized 1-harmonic equations (1.1). Using some ideas and techniques in studying 1-harmonic functions from [W1] (2007), and in studying nonhomogeneous 1-harmonic functions on a cocompact set from [W2, (9.1)] (2008), we find an analytic quantity w in the generalized 1-harmonic equatio…
TgAE constructs surrogates for inverse modeling with theory-guided training.
problem Creating accurate surrogates for inverse modeling with limited data.
method Theory-guided Auto-Encoder (TgAE) framework based on CNN architecture.
result TgAE surrogate achieves satisfactory accuracy and efficiency in uncertainty quantification and parameter inversion.
In this note, we extend our previous work on the inverse σk problem. Inverse σk problem is a fully nonlinear geometric PDE on compact Kähler manifolds. Given a proper geometric condition, we prove that a large family of nonlinear geometric flows converges to the desired solution of the given PDE.
Sliced Inverse Regression reduces parameter space for estimating complex financial models.
problem High-dimensional parameter space in stochastic differential equations.
method Sliced Inverse Regression for dimension reduction.
result Reduced computational costs in estimating parameters.
Study applies inverse scattering to BKM systems, linking spectra and integrable systems.
problem Applying inverse scattering to BKM systems.
method Developed methods for BKM systems, relating Schrödinger-Hill operators, Neumann system, and KdV equations.
result Initial observations indicate potential for applying inverse scattering to BKM systems.
Develops a neural network approach to solve inverse stochastic problems from particle observations.
problem Inference of Fokker-Planck equation coefficients from sparse particle data.
method Physics-informed neural networks (PINNs) with Kullback-Leibler divergence loss.
result Simultaneous inference of Fokker-Planck equation and multi-dimensional PDF from few particle observations.
We study positivity in the conjecture proposed by Lejmi and Székelyhidi on finding effective necessary and sufficient conditions for solvability of the inverse σk equation, or equivalently, for convergence of the inverse σk-flow. In particular, for the inverse σn−1-flow we partially verify their conjecture b…
Variational Gaussian Processes solve linear inverse problems efficiently.
problem Solving inverse problems where indirect observations are corrupted by noise.
method Variational Bayesian methods with Gaussian process priors and inducing variables.
result Posterior contraction rates can be attained by correctly tuned variational procedures.
Study on heat flow across two half-lines with special boundary conditions.
problem Low energy mode of heat flow transmission across a Grushin-type cylinder.
method Analysis of heat equation with inverse-square potential and bridging boundary conditions.
result First insight into qualitative features of the heat flow solution at later times.
Proves smooth solutions for generalised Monge-Ampère equations on projective manifolds.
problem Existence of smooth solutions for generalised Monge-Ampère equations on projective manifolds.
method Intersection numbers and degenerate concentration of mass result.
result Proves existence of smooth solutions for generalised Monge-Ampère equations on projective manifolds.
We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem and prove that the …
Study determines minimal surfaces from boundary data, proving topological and conformal recoverability.
problem Determining minimal surfaces from boundary data.
method Developed a semiclassical nonlinear calculus for complex geometric optics solutions.
result Minimal surfaces can be recovered from the Dirichlet-to-Neumann map under certain conditions.
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
TNet combines DL with physics models to solve inverse problems efficiently.
problem Solving inverse problems with limited data and physics constraints.
method Model-constrained deep learning approach using TNet.
result TNet solutions are as accurate as traditional methods but faster.
Study determines a minimal surface in a Riemannian manifold from boundary data.
problem Determining a minimal surface in a Riemannian manifold from boundary data.
method Analyzes the Dirichlet-to-Neumann map for the minimal surface equation.
result Knowledge of the Dirichlet-to-Neumann map determines the Riemannian manifold up to isometry.
Unified framework for forward and inverse PDE problems in multiphase media.
problem Non-differentiable inverse problems in discrete-valued material fields.
method GenPANIS: Latent-variable generative framework preserving discrete microstructures.
result Unified bidirectional inference with minimal labeled pairs and physics-aware decoder.
ML surrogates speed up Bayesian inverse problem solving.
problem Infer source location from noisy acoustic wave equation data.
method Use neural network as surrogate for PDE, apply MCMC to posterior.
result Accurately infers source location from noisy data.
New method reduces variance in Bayesian inverse problems.
problem High variance in Monte Carlo estimates for inverse problems.
method Conditional neural control variates based on Stein's identity.
result Substantial variance reduction across different inverse problems.
A new simulation method for Volterra processes improves convergence for rough kernels.
problem Simulating Volterra processes with singular kernels.
method iVi (integrated Volterra implicit) scheme based on Inverse Gaussian distribution.
result The iVi scheme achieves weak convergence with few time steps, especially for rough kernels.