Related papers: Robust inversion of time-resolved data via forward…
The possibility to have results very quickly after, or even during, the collection of electromagnetic data would be important, not only for quality check purposes, but also for adjusting the location of the proposed flight lines during an…
Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension.…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
This paper addresses a difficult inverse problem that involves the reconstruction of a three-dimensional model of tetrahedral amorphous semiconductors via inversion of diffraction data. By posing the material-structure determination as a…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…
Accurate modeling of ultrasound wave propagation is essential for high-fidelity simulation and imaging in ultrasonic testing. A primary challenge lies in characterizing the excitation source, particularly for transducers with large…
This paper develops a data-driven time-limited h2 model reduction method for discrete-time linear time-invariant systems. Specifically, we formulate and solve a regularized time-limited h2 model reduction problem using only noisy impulse…
In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can…
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…
The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…
Inversion of electromagnetic data finds applications in many areas of geophysics. The inverse problem is commonly solved with either deterministic optimization methods (such as the nonlinear conjugate gradient or Gauss-Newton) which are…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex…
To exploit the thousand-fold increase in spectral brightness of modern light sources, increasingly intricate experiments are being conducted that demand extremely precise beam trajectory. Maintaining the optimal trajectory over several…
Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…
An approach is presented for the inversion of simulated and experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a…
In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson-Lucy iterative deconvolution as fixed-point iteration for the…