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We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
This work presents a framework to inversely quantify uncertainty in the model parameters of the friction model using earthquake data via the Bayesian inference. The forward model is the popular rate- and state- friction (RSF) model along…
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…
Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the {\it spectral} support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable…
Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…
An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or…
Machine learning algorithms often struggle to control complex real-world systems. In the case of nuclear fusion, these challenges are exacerbated, as the dynamics are notoriously complex, data is poor, hardware is subject to failures, and…