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Advanced geometrical nanometrology is critical for process control in semiconductor manufacturing, supporting applications in, e.g., photonic integrated circuits, nanoelectronics, and emerging quantum and optoelectronic technologies.…
Background and purpose: In-beam Positron Emission Tomography (PET) is one of the modalities that can be used for in-vivo non-invasive treatment monitoring in proton therapy. PET distributions obtained during various treatment sessions can…
This thesis examines the empirical mode decomposition (EMD), a method for decomposing multicomponent signals, from a modern, both theoretical and practical, perspective. The motivation is to further formalize the concept and develop new…
We explore the potential of optical intensity interferometry to extract angularly resolved information from supernova explosions, introducing the "expanding ejecta method" (EEM) as a robust alternative to the classical expanding photosphere…
Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of the linear Extended Proper Orthogonal…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Let $F$ be a compact set of a Banach space $\mathcal{X}$. This paper analyses the "Generalized Empirical Interpolation Method" (GEIM) which, given a function $f\in F$, builds an interpolant $\mathcal{J}_n[f]$ in an $n$-dimensional subspace…
The empirical mode decomposition (EMD) method and its variants have been extensively employed in the load and renewable forecasting literature. Using this multiresolution decomposition, time series (TS) related to the historical load and…
We present a comparison of the modal-decomposition based field solver MINERVA to the grid-based solver GENESIS. The modal decomposition used employs a set of fixed-width, zero-curvature Gaussian modes, as opposed to the more-commonly used…
An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
Exploring the capabilities of Neural Radiance Fields (NeRF) and Gaussian-based methods in the context of 3D scene reconstruction, this study contrasts these modern approaches with traditional Simultaneous Localization and Mapping (SLAM)…
Incrementally recovering real-sized 3D geometry from a pose-free RGB stream is a challenging task in 3D reconstruction, requiring minimal assumptions on input data. Existing methods can be broadly categorized into end-to-end and visual…
All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent…
In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics…
Dispersion decomposes compound light into monochromatic components at different spatial locations, which needs to be eliminated in imaging but utilized in spectral detection. Metasurfaces provide a unique path to modulate the dispersion…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…
Gaussian boson sampling (GBS) has emerged as a promising quantum computing paradigm, demonstrating its potential in various applications. However, most existing works focus on theoretical aspects or simple tasks, with limited exploration of…