Related papers: Quantifying parameter uncertainties in optical sca…
Mathematical solvers use parametrized Optimization Problems (OPs) as inputs to yield optimal decisions. In many real-world settings, some of these parameters are unknown or uncertain. Recent research focuses on predicting the value of these…
Being able to rigorously quantify the uncertainties in reaction models is crucial to moving this field forward. Even though Bayesian methods are becoming increasingly popular in nuclear theory, they are yet to be implemented and applied in…
The nuclear matter parameters (NMPs), those underlie in the construction of the equation of state (EoS) of neutron star matter, are not directly accessible. The Bayesian approach is applied to reconstruct the posterior distributions of NMPs…
Purpose: Optical imaging is evolving as a key technique for advanced sensing in the operating room. Recent research has shown that machine learning algorithms can be used to address the inverse problem of converting pixel-wise multispectral…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…
Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty…
In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…