Computer algebra systems work with exact computations from various fields within Mathematics. In recent years computations that have previously seemed impossible have now become possible. This does not come without challenges. As the input and output data have now become too large for humans to handle, the resulting computations are run in parallel thus affecting runtime, which can take up to several months. In turn, there is now a need to affirm the accuracy of the results generated and to digest the results of these computations. Thus, the focus of TA1 will be to establish confirmable workflows, data formats and databased for computer algebra ensuring a degree of standardisation that is beneficial to developers and publishing companies within the mathematical community.

Members:

• TU Berlin (TUB)
• TU Kaiserslautern (TUKL)

Learn more about the Task Area Computer Algebra within MaRDI

Scientific computing is a cross-disciplinary topic bordering applied mathematics, computational sciences and engineering (CSE), as well as other scientific areas involving numerical computations like digital humanities or computational medicine. The principal data types involved are fixed precision real numbers that are prone to roundoff errors during copmutation. Beyond the data types found in engineering, such as input/output data of numerical software, in computational mathematics, and specifically in scientific computing, including the algorithms, implementations, procedural data, and their metadata descriptions are research data.

TA2 will focus on establishing knowledge graphs of numerical algorithms and open interfaces for their seamless interconnection in scientific computations. A benchmark framework employs both to asses their performance on a collection of reference data sets from their corresponding area of application, while following standardized workflows identified in collaboration with TA4 and other consortia.

Research within statistics and machine learning focuses on the development of broadly applicable methods for data analysis that solve prediction problems, support decision-making, and infer structure underlying a scientific phenomenon. Although these methods draw from computational techniques from TA1 and TA2, data in TA3 is inherently uncertain. Separating stochastic noise from the signal of interest is a key challenge that arises in virtually all branches of sciences and engineering. Addressing this challenge is a chief goal of statistics and machine learning. TA3 will initiate libraries of curated datasets and their statical analyses, which will be connected to software and research literature through an associated library of statistical analyses. It will set up tools to support the process of benchmarking experiments and peer-review of numerical experiments.

As mathematical model data, software and workflows can be applied in a wide range of disciplines from natural to life sciences and the humanities, the digitization of research data is seen as the main stronghold of mathematics. This together with the standardization of data within the NFDI framework would emulate the FAIR principles and allow a dependable platform from which other disciplines could benefit from. Working from case studies, TA4 aims to work together with interdisciplinary partners and other NFDI consortia to develop interdisciplinary workflows, standardize mathematical descriptions and create a platform for exchange.

Currently, most of the available knowledge, research data and services are hosted as individual solutions in a silo-like fashion. This makes data difficult to find, access and reproduce. The aim of this task area is to develop, implement and maintain a user-friendly way to make mathematical knowledge, research data and services digitally available and accessible to the scientific community. The portal will become a one-stop contact point housing newly developed and existing external resources, which will be integrated into the MaRDI knowledge graphs and made accessible. It will also serve as a repository for large research datasets and mathematical services such as algorithms and workflow executions.

Developing and establishing a common data culture is the core objective of MaRDI. Hence, this TA is designed to engage with and support both the German and international mathematical communities. It does so by integrating mathematicians, data specialists, and the general public through workshops, data consultancy, and interactive dissemination.

The main aim of this is to TA organize and support the governance structure and duties of various boards within MaRDI. Aside from this, it will also manage the overall progress of MaRDI through the coordination and arrangement of regular meetings within the consortium, workshops with both internal and external user groups, new participants and interest groups.