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A novel concept of self-phasematched optical frequency conversion in dispersive dielectric microcavities is studied theoretically and experimentally. We develop a time-dependent model, incorporating the dispersion into the structure of the…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
The use of multimode fibers offers advantages in the field of communication technology in terms of transferable information density and information security. For applications using physical layer security or mode division multiplexing, the…
A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys., submitted]. The…
Multimode fiber imaging requires strict matching between measurement value and measurement matrix to achieve image reconstruction. However, in practical applications, the measurement matrix often cannot be obtained due to unknown system…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
Multi-mode fibers provide an increased amount of data transfer rates given a large number of transmission modes. Unfortunately, the increased number of modes in a multi-mode fiber hinders the accurate transfer of information due to…
This report addresses the maximum likelihood identification of models for offset-free model predictive control, where linear time-invariant models are augmented with (fictitious) uncontrollable integrating modes, called integrating…
This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
We demonstrate the use of deep learning for fast spectral deconstruction of speckle patterns. The artificial neural network can be effectively trained using numerically constructed multispectral datasets taken from a measured spectral…
Optical computing has gained significant attention as a potential solution to the growing computational demands of machine learning, particularly for tasks requiring large-scale data processing and high energy efficiency. Optical systems…
This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…
A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge…
This paper studies the inverse problem related to the identification of the flexural stiffness of an Euler Bernoulli beam in order to reconstruct its profile starting from available response data. The proposed identification procedure makes…