Across disciplines, current challenges in sciences ask for a relief from computational limitations caused by the complexity of multi-dimensional systems.
Recently Dr. Michael Hecht found a notion of unisolvent nodes. On this basis the 1D Newton & Lagrange interpolation schemes (developed 300 years ago) could be generalised to arbitrary dimensions. As it turns out, this discovery allows to lift the curse of dimensionality from classical computational schemes as numerical integration, fast Fourier transforms, ODE & PDE solvers, linear/polynomial regression etc.
The 2nd CASUS Multivariate Interpolation Workshop in March 2020 aimed to implement and test prototype solvers for the mentioned computational problems and directly test them on experimental data.
The participants developed and implemented new computational methods including:
• Polynomial Interpolation on scattered data in multi—dimensions
• Polynomial Regression & Denoising in multi-dimensions
• Tight metrics that control the phase retrieval quality
• Fast parameter tuning for adaptive optics
• Concepts for distributed Fast Fourier Transforms
• Regularisation of machine learning on deep neural nets
• PDE Learning and Simulation by machine learning methods
The implemented code and documentations are uploaded at the HZDR GitLab.
For questions and further details please contact: hecht@mpi-cbg.de
Organizer: Dr. Michael Hecht