Hi all, it’s that time of year again! GSOC 2021 is around the corner so we need to add our project ideas for this year to the NumFOCUS site here. Before we do that, perhaps we can brainstorm ideas here!
Below is an editable list of project ideas:
Enhancing visualisation and tutorials: Visualising various equadratures objects, and their underlying data, is a crucial task in many equadratures use cases. To reduce the amount of boilerplate code required for visualisations we have started developing in-built plotting methods. This project would involve enchancing this capability, which might include expanding the range of plotting methods and improving user customisation. Updating our tutorials to show off this new user-friendly capability would also be an important part of the project. Depending on the students interests, there is also the possibility of exploring interactive visualisation with libraries such as bokeh or plotly, or even interactive web apps with streamlit or similar tools.
Universal quadrature repository: Delivering accurate quadrature rules—for numerical integration—remains one of the key tenets of Effective Quadratures. While there has been much research, particularly into high-dimensional numerical integration, no universal repository of such quadrature rules exists. In this project, we wish to lay the foundations for such a universal repository of numerical integration rules.
Regularisation of polynomials: The double descent phenomenon has seen increasing attention in the machine learning community in recent years. It contradicts the classic bias-variance tradeoff concept, and has important implications for how we build models which can generalise to test data effectively. It is desirable to avoid the double descent behavior, and have test error decrease monotonically with increased model complexity and/or increased amounts of training data. One way to achieve this is by adding regularisation, which if optimally tuned can mitigate double descent in many learning algorithms, from neural networks to linear regression. This project will involve validating and then optimising the elastic-net regularisation solver implemented within equadratures. Improving the performance of this solver would allow for larger real-world supervised ML datasets to be tackled.