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Quality-Diversity (QD) optimization algorithms are a well-known approach to generate large collections of diverse and high-quality solutions. However, derived from evolutionary computation, QD algorithms are population-based methods which…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
We propose a new method for fine registering multiple point clouds simultaneously. The approach is characterized by being dense, therefore point clouds are not reduced to pre-selected features in advance. Furthermore, the approach is robust…
Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…
Static program analysis today takes an analytical approach which is quite suitable for a well-scoped system. Data- and control-flow is taken into account. Special cases such as pointers, procedures, and undefined behavior must be handled. A…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
In this paper we introduce the Diagonal Dominant Pole Spectrum Eigensolver (DDPSE), which is a fixed-point method that computes several eigenvalues of a matrix at a time. DDPSE is a slight modification of the Dominant Pole Spectrum…
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
The goal of point cloud assembly is to reconstruct a complete 3D shape by aligning multiple point cloud pieces. This work presents a novel equivariant solver for assembly tasks based on flow matching models. We first theoretically show that…
Unsupervised domain adaptation (DA) with the aid of pseudo labeling techniques has emerged as a crucial approach for domain-adaptive 3D object detection. While effective, existing DA methods suffer from a substantial drop in performance…
Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…
In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…
The Distribution Matching Distillation (DMD) has been successfully applied to text-to-image diffusion models such as Stable Diffusion (SD) 1.5. However, vanilla DMD suffers from convergence difficulties on large-scale flow-based…
Quantum error correction is one of the most important milestones for realization of large-scale quantum computation. To achieve this, it is essential not only to integrate a large number of qubits with high fidelity, but also to build a…
High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…