Applications of Topological Data Analysis to Cosmology and Beyond

Jun 5, 2023, 9:00 AM → Jun 9, 2023, 4:00 PM Europe/Rome

305 (IFPU)

Matteo Biagetti (SISSA)

The workshop is organized as a "Team Research Week", these are small group meetings with the aim of developing or finalizing research projects. We are a group of 6-7 researchers who have been working on solving specific inference and computational problems related to cosmological data using topological data analysis. The format of the workshop will be very informal: we'll have a few talks and many sessions for working in small groups and making progress on the projects. A tentative list of topics will cover:

1. Generative models for cosmological simulations
2. Information Maximizing Persistent Homology
3. Parameter inference using persistent homology
4. Multiparameter persistence

Given the potential overlap with activities in the area, the meeting is open to everyone interested, and we'll have a specific day dedicated to fostering collaboration with external people interested in knowing more about the topic.

Monday, June 5

9:30 AM Registration and Coffee

1 Introduction to Workshop

Speaker: Matteo Biagetti (SISSA)

2 Persistent Homology of Cosmic Structures

Speaker: Matteo Biagetti

3 Information Maximizing Persistent Homology

Speaker: Karthik Viswanathan

12:00 PM Hands-on collaboration and free time

1:00 PM Lunch @ICTP

4 Unsupervised learning methods in quantum computers and simulators: why we do it and which methods have been used

Speaker: Marcello Dalmonte

3:00 PM Hands-on collaboration and free time

Tuesday, June 6

5 Parameter inference using persistent homology

Speaker: Sibilla Bouché

10:30 AM Coffee Break

11:00 AM Hands-on collaboration and free time

12:30 PM Lunch @ ICTP

6 Quasars and/or dimensionality reduction

Speaker: Gabriella Contardo

7 Our Attempts to Use Unsupervised Learning in Soft-Matter Physics

Speaker: Ali Hassanali

4:00 PM Hands-on collaboration and free time

Wednesday, June 7

8 An introduction to Topological Data Analysis

Topological Data Analysis (TDA) is a growing field of research at the intersection of data science and computational geometry and topology. It has encountered key successes in several different applications (ranging from cancer subtype identification in bioinformatics to shape recognition in computer vision, just to name a few), and become the landmark product of several companies in the recent years. Indeed, many data sets nowadays come in the form of point clouds embedded in very large dimensional spaces, yet concentrated around low-dimensional geometric structures that need to be uncovered. Unraveling these structures is precisely the goal of TDA, which can build descriptors that can reliably capture geometric and topological information (connectivity, loops, holes, curvature, etc.) from the data sets without the need for an explicit mapping to lower-dimensional space. This is extremely useful since the hidden, non-trivial topology of many data sets can make it very challenging to perform well for classical techniques in data science and machine learning, such as dimensionality reduction.

In this talk, I will provide a global overview of TDA, by introducing its main descriptors and by presenting the theoretical guarantees that they enjoy. I will also show how they can be efficiently computed in practice with the dedicated, open-source library GUDHI, and describe some applications where TDA proved useful.

Speaker: Mathieu Carrière

10:30 AM Coffee break @ ICTP bar

9 On the geometry of large transformers representations

Speaker: Alberto Cazzaniga

10 Barcodes for multiparameter persistence

Multiparameter persistence is a generalization of persistent homology that allows for more than a single filtration function. Such constructions arise naturally when considering data with outliers or variations in density, time-varying data, or functional data.

In single-parameter persistence, the barcode is equivalent to the “rank invariant”: the function that associates the rank of the corresponding linear map to every pair of comparable points. However, nearly all of the tools developed in persistent homology are based on the barcode. This is because it is a concise and geometric descriptor that lends well to data analysis and visualization. Therefore, it is crucial, and perhaps imperative, to construct a generalized barcode to work with the rank-invariant for multiparameter persistence efficiently.

Perhaps surprisingly, recent work has shown that if we allow the elements of the barcode to be signed intervals, then such a generalization is possible. I will discuss how one can use homological algebra to obtain a signed barcode in a stable manner. Furthermore, I will discuss how signed barcodes can be used in machine learning and report on recent computational results.

Speaker: Magnus Botnan

1:00 PM Lunch @ ICTP

11 What Every Physicist Should Know About String Theory

This event is organized by ICTP.

Speaker: Edward Witten

3:00 PM Coffee Break

12 Machine learning you can trust for cosmology and astrophysics

Speaker: Roberto Trotta

Thursday, June 8

13 Multiparameter persistence

Speaker: Sliem El Ela

10:30 AM Coffee Break

11:00 AM Hands-on collaboration and free time

12:30 PM Lunch

14 Graph-based algorithms

15 Inverse optimization

Speaker: Sliem El Ela

3:30 PM Hands-on collaboration and free time

Friday, June 9

16 Generative models for cosmological simulations

Speaker: Mathieu Carrière

10:30 AM Coffee Break

11:00 AM Hands-on collaboration and free time

12:30 PM Lunch

17 Closing remarks