Related papers: Posterior error bounds for prior-driven balancing …
The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…
Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero…
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance…
A way to lower computational cost in large scale inverse problems and problems depending on poorly known model parameters is to replace the detailed model by an approximate one. Inverse problems are typically ill-posed, and the model…
This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…
We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…
In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et al. (2020), where it is shown that in such a setting the…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors.…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…