Related papers: Freeform imaging systems: Fermat's principle unloc…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extended here to instant- and…
Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
What is a diffusion model actually doing when it turns noise into a photograph? We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that this framework serves as a unified design…
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or…
Curved and conformal optics offer significant advantages by unlocking additional geometric degrees of freedom for optical design. These capabilities enable enhanced optical performance and are essential for meeting non-optical constraints,…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
The free-form deformation model can represent a wide range of non-rigid deformations by manipulating a control point lattice over the image. However, due to a large number of parameters, it is challenging to fit the free-form deformation…
Metasurfaces, with their ability to control electromagnetic waves, hold immense potential in optical device design, especially for applications requiring precise control over dispersion. This work introduces an approach to dispersion…
We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…
We report a novel generalized optical measurement system and computational approach to determine and correct aberrations in optical systems. We developed a computational imaging method capable of reconstructing an optical system's…
This contribution is concerned with the motion planning for underactuated Euler-Bernoulli beams. The design of the feedforward control is based on a differential parametrization of the beam, where all system variables are expressed in terms…
Optical imaging systems are inherently imperfect due to diffraction limits, lens manufacturing tolerances, assembly misalignment, and other physical constraints. In addition, unavoidable camera shake and object motion further introduce…
In recent years, mode-division multiplexing (MDM) has been proposed as a promising solution in order to increase the information capacity of optical networks both in free-space and in optical fiber transmission. Here we present the design,…
We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample's typical feature size. Quantitative…
Fourier ptychographic microscopy (FPM) is a recently developed computational imaging technique for wide-field, high-resolution microscopy with a high space-bandwidth product. It integrates the concepts of synthetic aperture and phase…
Imaging through diffusers presents a challenging problem with various digital image reconstruction solutions demonstrated to date using computers. We present a computer-free, all-optical image reconstruction method to see through random…
We use a spatial light modulator in a diffraction tomographic system to assess the accuracy of different refractive index reconstruction algorithms. Optical phase conjugation principles through complex media, allows us to quantify the error…