Natural computation techniques for uncovering low-dimensional topological structures in large scale astronomical simulations

During my PhD studies, I collaborated in an exciting project between astronomeers and computer scientists. We developed machine learning strategies to detect, extract, and denoise manifolds embedded in potentially large amounts of background noise in higher dimensions. Examples of such a dataset are filaments in an N-body simulation of the Cosmic web or streams of a jellyfish-like dwarf galaxy. Furthermore, we proposed a subsampling technique that preserves the crucial topological information of large astronomical datasets. Extracting information from large data sets, such as discovering bubbles in a dwarf galaxy simulation, is often resource-demanding. As a result, the proposed subsampling is of utmost importance. Besides, to further continue the study, the position of particles on the border of bubbles should be determined. We also suggest a pipeline to recover a tight boundary around each bubble and finally, we conduct an extensive analysis of the temperature, velocity of expansion, age, and other physical features of the discovered bubbles through several snapshots of the dwarf galaxy simulation

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov

LAAT: Locally Aligned Ant Technique for discovering multiple faint low dimensional structures of varying density

Dimensionality reduction and clustering are often used as preliminary steps for many complex machine learning tasks. The presence of noise and outliers can deteriorate the performance of such preprocessing and therefore impair the subsequent analysis tremendously. In manifold learning, several studies indicate solutions for removing background noise or noise close to the structure when the density is substantially higher than that exhibited by the noise. However, in many applications, including astronomical datasets, the density varies alongside manifolds that are buried in a noisy background. We propose a novel method to extract manifolds in the presence of noise based on the idea of Ant colony optimization. In contrast to the existing random walk solutions, our technique captures points that are locally aligned with major directions of the manifold. Moreover, we empirically show that the biologically inspired formulation of ant pheromone reinforces this behavior enabling it to recover multiple manifolds embedded in extremely noisy data clouds. The algorithm performance in comparison to state-of-the-art approaches for noise reduction in manifold detection and clustering is demonstrated, on several synthetic and real datasets, including an N-body simulation of a cosmological volume

1-DREAM: 1D Recovery, Extraction and Analysis of Manifolds in noisy environments

Filamentary structures (one-dimensional manifolds) are ubiquitous in astronomical data sets. Be it in particle simulations or observations, filaments are always tracers of a perturbation in the equilibrium of the studied system and hold essential information on its history and future evolution. However, the recovery of such structures is often complicated by the presence of a large amount of background and transverse noise in the observation space. While the former is generally considered detrimental to the analysis, the latter can be attributed to measurement errors and it can hold essential information about the structure. To further complicate the scenario, one-dimensional manifolds (filaments) are generally non-linear and their geometry difficult to extract and model. Thus, in order to study hidden manifolds within the dataset, particular care has to be devoted to background noise removal and transverse noise modeling, while still maintaining accuracy in the recovery of their geometrical structure. We propose 1-DREAM: a toolbox composed of five main Machine Learning methodologies whose aim is to facilitate manifold extraction in such cases. Each methodology has been designed to address particular issues when dealing with complicated low-dimensional structures convoluted with noise and it has been extensively tested in previously published works. However, for the first time, in this work all methodologies are presented in detail, joint within a cohesive framework and demonstrated for three particularly interesting astronomical cases: a simulated jellyfish galaxy, a filament extracted from a simulated cosmic web and the stellar stream of Omega-Centauri as observed with the GAIA DR2. Two newly developed visualization techniques are also proposed, that take full advantage of the results obtained with 1-DREAM. This contribution presents the toolbox in all its details and the code is made publicly available to benefit the community. The controlled experiments on a purposefully built data set prove the accuracy of the pipeline in recovering the real underlying structures