Related papers: Parameterizations for Ensemble Kalman Inversion
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of properties of the subsurface which can be used to aid structural interpretation alongside the…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…
This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF), thereby yielding a multilevel ensemble Kalman filter (MLEnKF) which has provably superior asymptotic cost to…
Level set method has been used to capture interface motion. Narrow band algorithm is applied to localize the solving of level-set PDE on global domain to a tube around interface. Due to the unknown evolving interface, narrow band algorithm…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can…
Data integration tasks such as the creation and extension of knowledge graphs involve the fusion of heterogeneous entities from many sources. Matching and fusion of such entities require to also match and combine their properties…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the…