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Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…
We investigate the accuracy of rigorous coupled wave analysis (RCWA) for near-field computations within cylindrical GaAs nanowire solar cells and discover excellent accuracy with low computational cost at long incident wavelengths, but poor…
Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…
We propose a micro-macro parallel-in-time Parareal method for scalar McKean-Vlasov stochastic differential equations (SDEs). In the algorithm, the fine Parareal propagator is a Monte Carlo simulation of an ensemble of particles, while an…
A retinal trait, or phenotype, summarises a specific aspect of a retinal image in a single number. This can then be used for further analyses, e.g. with statistical methods. However, reducing an aspect of a complex image to a single,…
The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. However, these tissue properties are spatially varying across the underlying anatomical model,…
The near-field effect of short-range multiple-input multiple-output (MIMO) systems imposes many challenges on direction-of-arrival (DoA) estimation. Most conventional scenarios assume that the far-field planar wavefronts hold. In this…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
Achieving high-precision light manipulation is crucial for delivering information through complex media with high fidelity. However, existing spatial light modulation devices face a fundamental tradeoff between speed and accuracy. Digital…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
Control of light through a microscope objective with a high numerical aperture is a common requirement in applications such as optogenetics, adaptive optics, or laser processing. Light propagation, including polarization effects, can be…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Few-shot object detection (FSOD) is challenging due to unstable optimization and limited generalization arising from the scarcity of training samples. To address these issues, we propose a hybrid ensemble decoder that enhances…
This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable.…
Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be designed with a few discrete frequencies hence allowing for compact volume of data to be managed. Moreover, attenuation effects can be…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
The main objective of the present project is to explore the viability of an adaptive optics control system based exclusively on Field Programmable Gate Arrays (FPGAs), making strong use of their parallel processing capability. In an…
It is well understood that Dynamic Time Warping (DTW) is effective in revealing similarities between time series that do not align perfectly. In this paper, we illustrate this on spectroscopy time-series data. We show that DTW is effective…