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Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
We develop a novel transfer learning framework to tackle the challenge of limited training data in image reconstruction problems. The proposed framework consists of two training steps, both of which are formed as bi-level optimizations. In…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
We propose in this work a fast numerical algorithm for solving the equation of radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first step, we derive an integral equation for the angularly averaged ERT…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
A new code for evaluation of light absorption and scattering by interstellar dust grains is presented. The radiative transfer problem is solved using ray-tracing algorithm in a self-consistent and highly efficient way. The code demonstrates…
We present the methodology of a photon-conserving, spatially-adaptive, ray-tracing radiative transfer algorithm, designed to run on multiple parallel Graphic Processing Units (GPUs). Each GPU has thousands computing cores, making them…
The 3D Gaussian splatting method has drawn a lot of attention, thanks to its high performance in training and high quality of the rendered image. However, it uses anisotropic Gaussian kernels to represent the scene. Although such…
Conventional rendering techniques are primarily designed and optimized for single-frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is…
Recent progress in large-scale scene rendering has yielded Neural Radiance Fields (NeRF)-based models with an impressive ability to synthesize scenes across small objects and indoor scenes. Nevertheless, extending this idea to large-scale…
Radio-frequency (RF) Radiance Field reconstruction is a challenging problem. The difficulty lies in the interactions between the propagating signal and objects, such as reflections and diffraction, which are hard to model precisely,…
In this paper we discuss numerical methods and algorithms for the solution of NLTE stellar atmosphere problems involving expanding atmospheres, e.g., found in novae, supernovae and stellar winds. We show how a scheme of nested iterations…
Radiative transfer describes the propagation of electromagnetic radiation through an interacting medium. This process is often simulated by the use of the Monte Carlo method, which involves the probabilistic determination and tracking of…
Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic…
Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective…
We present a new numerical method for transporting arbitrary sets in a velocity field. The method computes a deformation mapping of the domain and advects particular sets by function composition with the map. This also allows for the…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not…