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 method uses neural networks to identify sources from limited data in complex systems.
problem Identifying sources from noisy and limited data in high-dimensional systems.
method Calibrating deep neural network surrogates to ensemble simulations and using Bayesian optimization for source identification.
result Reliable source identification with uncertainty quantification using limited data and auxiliary processes.
Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates d…
The identification of sources of advection-diffusion transport is based usually on solving complex ill-posed inverse models against the available state- variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influ…
A new algorithm speeds up EEG source localization using ℓ1 regularization.
problem Challenging inverse problem in mapping EEG readings to brain activity.
method Formulated as a graphical generalized elastic net inverse problem, solved with a variable projected algorithm (VPAL).
result VPAL provides faster and more accurate EEG source localization compared to existing methods.
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.
A new machine learning method for Bayesian inverse problems in function spaces.
problem Bayesian inverse problems in function spaces with incompatibility of white noise sources.
method One-step generative transport with amortized neural operator and prior-aligned Gaussian random field.
result Generative operator trained on prior samples and noisy observations generates posterior samples efficiently.
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.
Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly finding the inverse of the model. The former class of techniques require explicit…
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+). Inverse Drum Machine separates drum mixes using transcription and synthesis.
problem Separating individual drum tracks from mixed recordings.
method Analysis-by-synthesis framework combining deep learning and automatic transcription.
result Separation quality comparable to supervised methods requiring isolated stems.
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
New approach transfers rewards learned in one environment to reinforcement learning in a new environment.
problem Transfer of rewards learned using inverse reinforcement learning from one environment to a new, different environment.
method Formulate the problem as a joint system of Bellman equations, develop minimax estimators for the target soft-q-function, solve the source and target system of equations jointly. result The coupled approach removes the first-order influence of source Bellman residual error compared to the sequential approach.
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…
A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.
problem Approximating posterior distributions in Bayesian inverse problems with intractable likelihoods.
method Proposes a mixture-based approximation of intermediate posterior distributions and uses Gibbs sampling for practical sampling.
result Validated the approach on image inverse problems and audio source separation, demonstrating improved performance.
The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.
problem Statistical inverse problems in Hilbert scales with general noise.
method Tikhonov regularization scheme with conditional stability estimates and high probability error bounds.
result Explicit rates of convergence for oversmoothing and regular cases over defined regularity classes.
Researchers reconstruct simple Riemannian manifolds from boundary wave arrival times.
problem Reconstructing Riemannian manifolds from unknown interior sources and arrival times.
method Discrete metric approximation using labeled Gromov--Hausdorff distance.
result Finite-time approximations converge to the true Riemannian manifold.
Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based surrogate method is developed for the forward model to allow us to solve efficien…
Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources, its application to rapid stimulation pulses, which contain more high-frequency pow…
We make posterior sampling in FWI feasible for large surveys.
problem Uncertainty-aware subsurface models at field scale.
method Coupling diffusion-based posterior sampling with simultaneous-source FWI data.
result Lower model error and better data fit at reduced computational cost.
New method improves source separation using adversarial NMF.
problem Improving source separation in single channel signals.
method Adversarial training of non-negative matrix factorization (NMF).
result Adversarial NMF leads to better signal reconstruction.
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.
In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by regularizing the solution in space and time by a Gaussian process (Gaussian random field)…
Study rates of convergence for approximate solutions to linear ill-posed problems in Hilbert scales.
problem Linear ill-posed inverse problems with noisy data.
method Approximate reconstructions from random noisy data using regularization schemes in Hilbert scale.
result Explicitly established error bounds for smooth regression functions.
Reconstructing Finsler manifolds from sphere data.
problem Recovering a Finsler manifold from sphere data.
method Solving the geometrical inverse problem locally along geodesics.
result Local reconstruction of Finsler manifolds.
We consider a statistical inverse learning problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points Xi, superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimati…
Fractional Laplacian inverse problem solved for connection Laplacians.
problem Determining structures from metric, bundle, and map knowledge.
method Local knowledge of metric, bundle, and map determines global structures.
result Global structures determined from local knowledge of metric, bundle, and map.
Proposes using Wasserstein barycenters for robust optimization with multiple data sources.
problem Distributionally robust optimization with multiple heterogeneous data sources.
method Construct nominal distribution through Wasserstein barycenter of multiple data samples, reformulates as a finite convex program.
result Proposed scheme outperforms other estimators in sparse inverse covariance matrix estimation.
Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear Modeling framework (GLM), used in this case to separate stochastic (Gaussian) noise…
Magnetoencephalography (MEG) and electroencephalogra-phy (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Inferring the location of the current sources that generated these magnetic fields is an ill-posed inverse problem known as source imaging. When consideri…
Bayesian method improves EEG source localization and estimates skull conductivity.
problem Improving EEG source localization accuracy with unknown skull conductivity.
method Bayesian Approximation Error approach using conditional Gaussian regression, iterative optimization, and physics-informed learning.
result Clear improvements in EEG source localization accuracy and feasible estimates for unknown skull conductivity.
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.
Study sparse function recovery from indirect noisy observations using ℓ1-regularization.
problem Recovering sparse functions from indirect, noisy observations.
method Proposes an ℓ1-regularized empirical risk minimizer and analyzes its statistical properties. result Established almost-sure consistency and derived high-probability convergence rates in prediction and ℓ1 norms. New neural network extracts signal components and their IFs from non-uniform samples.
problem Recovering signal components and their IFs from discrete blind-source data.
method Inspired by theory, deep neural network extends Hilbert transform and synchrosqueezed wavelet transform.
result Neural network resolves inverse problem for non-uniformly sampled 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.
Framework solves physics-constrained inverse problems with limited data.
problem Physics-constrained inverse problems with scarce training data.
method Conditional flow matching for Bayesian inverse problems.
result Conditional flow matching mitigates degeneracy in finite training data.
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation …
Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that…
Given a bounded domain M in Rn with a conformally Euclidean metric g=ρdx2, in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain Γ⊂∂M and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Carte…
DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatia…
Paper proposes hybrid modeling to improve surrogate accuracy using multiple data sources.
problem Improving surrogate model accuracy by integrating simulation and real-world data.
method Two novel probabilistic approaches: separate and combined surrogates with weighting strategy.
result Hybrid models improve predictive accuracy and coverage compared to single-source surrogates.
We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that Γ1 and Γ2 are two disjoint open subsets of the boundary of the manifold we define the restricted Dirichlet-to-Neumann operator ΛΓ1,Γ2. This operator corresponds the boundary measure…
The paper reformulates regression in infinite dimensions as an inverse problem, showing it's equivalent to compact inverse problems.
problem Learning a linear operator between Hilbert spaces from empirical observations.
method Reformulates regression as an inverse problem, proving equivalence to compact inverse problems under specific conditions.
result The inverse problem is equivalent to compact inverse problems in terms of spectral properties and regularisation theory.
The Reeb space of a smooth map whose codimension is minus is the space defined as the space of all connected components of inverse images. For generic maps such as Morse functions and their higher dimensional versions, they are polyhedra whose dimensions are equal to those of the target manifolds and which have simplic…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-…
Neural Empirical Bayes estimates source distributions from noisy simulations.
problem Estimating source distributions from noisy, simulated data.
method Uses neural density estimators to estimate a prior or source distribution over uncorrupted samples, then performs posterior inference.
result Recovering ground truth source distributions up to symmetries.
Reconstructing manifolds from partial distance and heat kernel data.
problem Reconstructing a manifold from noisy distance measurements and heat kernel data.
method Approximate reconstruction of a manifold from partial distance and heat kernel data with noise.
result A stable reconstruction of the manifold can be achieved from noisy heat kernel data.