Related papers: The extended adjoint state and nonlinearity in cor…
We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical…
Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models…
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…
This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and…
Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the…
Passive imaging refers to problems where waves generated by unknown sources are recorded and used to image the medium through which they travel. The sources are typically modelled as a random variable and it is assumed that some statistical…
We present a methodology to model articulated objects using a sparse set of images with unknown poses. Current methods require dense multi-view observations and ground-truth camera poses. Our approach operates with as few as four views per…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
A particularly simple setup is introduced to study the influence of time-delayed coherent feedback on the optical squeezing properties of the degenerate parametric amplifier (DPA). The possibility for significantly enhanced squeezing is…
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…
There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics.…
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that arises in various research areas, e.g. fluid dynamics and…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…