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Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…

Recent advances in 3D Gaussian Splatting (3DGS) have focused on accelerating optimization while preserving reconstruction quality. However, many proposed methods entangle implementation-level improvements with fundamental algorithmic…

3D Gaussian Splatting (3DGS) has become a state-of-the-art framework for real-time, high-fidelity novel view synthesis. However, its substantial storage requirements and inherently unstructured representation pose challenges for deployment…

Accurate and consistent construction of point clouds from LiDAR scanning data is fundamental for 3D modeling applications. Current solutions, such as multiview point cloud registration and LiDAR bundle adjustment, predominantly depend on…

A multiverse analysis evaluates all combinations of "reasonable" analytic decisions to promote robustness and transparency, but can lead to a combinatorial explosion of analyses to compute. Long delays before assessing results prevent users…

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…

Visual SLAM algorithms achieve significant improvements through the exploration of 3D Gaussian Splatting (3DGS) representations, particularly in generating high-fidelity dense maps. However, they depend on a static environment assumption…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

We propose a novel multilinear dynamical system (MLDS) in a transform domain, named $\mathcal{L}$-MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one…

Advancements in artificial active matter heavily rely on our ability to characterise their motion. Yet, the most widely used tool to analyse the latter is standard wide-field microscopy, which is largely limited to the study of…

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

In this paper, we explore the capabilities of multimodal inputs to 3D Gaussian Splatting (3DGS) based Radiance Field Rendering. We present LiDAR-3DGS, a novel method of reinforcing 3DGS inputs with LiDAR generated point clouds to…

Detection and modeling of change-points in time-series can be considerably challenging. In this paper we approach this problem by incorporating the class of Dynamic Generalized Linear Models (DGLM) into the well know class of Product…

We present the MDS feature learning framework, in which multidimensional scaling (MDS) is applied on high-level pairwise image distances to learn fixed-length vector representations of images. The aspects of the images that are captured by…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

This work develops a fast, memory-efficient, and general algorithm for accelerated/undersampled dynamic MRI by assuming an approximate LR model on the matrix formed by the vectorized images of the sequence. By general, we mean that our…