Challenges in Preservation of Structure (CHiPS)
Welcome to the MSCA-RISE project Challenges in Preservation of Structure (CHiPS), supported by the EU Horizon 2020 program.
In this project we will address Challenges in Preservation of Structure for the numerical solution of evolutionary problems. There are two essential tools necessary to solve scientific problems on a computer:
- mathematical models, often consisting of differential equations
- numerical methods
Since the 1940s much attention has been devoted to the best ways to discretize differential equations so that they can be solved numerically. Initially, the main emphasis was on all-purpose methods (defined for all differential equations), such as Runge-Kutta methods and linear multistep methods, and their quantitative accuracy. During the last 25 years, however, interest has expanded to considering special classes of differential equations and purpose-built algorithms that are tailored to preserve the special features of each class. In addition to be quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate. This has resulted in methods that preserve symmetries, first integrals, symplectic structure, measure, foliations, Lyapunov functions, etc. These methods are called geometric integration methods.
The present project will address fundamental questions in the field of structure preserving algorithms. The research objectives for the CHiPS project include:
- analysis of algebraic, combinatorial and geometric structures underlying geometric numerical integration schemes for differential equations,
- structure preservation in partial differential equations with highly oscillatory solutions,
- new energy-dissipative techniques for image processing,
- geometric integration methods for Bayesian statistics,
- structure preserving methods for applications in mechanics and control.
Partners involved in the program.
| || |
The scientific innovations of the project will be incorporated into usable software tools in cooperation with our non-academic partner MathWorks.
CHiPS Video https://www.youtube.com/watch?v=CNN2XkC0hA8
Shape analysis in Lie groups and homogeneous manifolds https://www.birs.ca/events/2017/5-day-workshops/17w5152/videos/watch/201706160903-Celledoni.html
Geometric integration and Kahan's method http://www.birs.ca/events/2017/5-day-workshops/17w5152/videos/watch/201706140902-Quispel.html
Integral preserving methods on moving grids https://www.birs.ca/events/2017/5-day-workshops/17w5152/videos/watch/201706151633-Owren.html
Connections in Geometric Numerical Integration http://www.birs.ca/events/2017/5-day-workshops/17w5152/videos/watch/201706131329-Munthe-Kaas.html
News and activities
Isaac Newton Institute programme
Variational methods and effective algorithms for imaging and vision Cambridge, UK, Aug - Dec 2017
Part of CHiPS mission is to make our research available to a wider community of researchers, professionals and the general public. Learn more about CHiPS outreach activities