Related papers: Applying Bayesian Inference and deterministic anis…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
A major challenge in materials science is the determination of the structure of nanometer sized objects. Here we present a novel approach that uses a generative machine learning model based on diffusion processes that is trained on 45,229…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…
Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
Finite element simulations are run by package design engineers to model design structures. The process is irreversible meaning every minute structural adjustment requires a fresh input parameter run. In this paper, the problem of modeling…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a 1-dimensional time-series, such a goal becomes challenging. A paradigmatic example is the…
Many inverse problems focus on recovering a quantity of interest that is a priori known to exhibit either discontinuous or smooth behavior. Within the Bayesian approach to inverse problems, such structural information can be encoded using…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
We tackle the problem of recovering a complex signal $\boldsymbol x\in\mathbb{C}^n$ from quadratic measurements of the form $y_i=\boldsymbol x^*\boldsymbol A_i\boldsymbol x$, where $\boldsymbol A_i$ is a full-rank, complex random…
We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…