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Recent studies show strong generative performance in domain translation especially by using transfer learning techniques on the unconditional generator. However, the control between different domain features using a single model is still…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
Inverse optimal control (IOC) is about estimating an unknown objective of interest given its optimal control sequence. However, truly optimal demonstrations are often difficult to obtain, e.g., due to human errors or inaccurate…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely…
Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…
Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
This paper is devoted to the uniqueness of inverse acoustic scattering problems with the modulus of near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields…
Despite significant progress in text-to-image diffusion models, achieving precise spatial control over generated outputs remains challenging. ControlNet addresses this by introducing an auxiliary conditioning module, while ControlNet++…