Nature abounds with mathematical structure. Computational models of nature, however, often do not reflect such structure, and hence their predictions may suffer. Structure-preserving discretizations are numerical methods that attempt to mimic mathematical structures or properties of the continuous system on the discrete (numerical) level. Such discretizations are often essential in order to maintain the accuracy and stability of simulations. Important applications whose predictions hinge on structure preservation include fusion and turbulence. These applications are linked to some of the most pressing current societal issues. Moreover, emergent applications that utilize machine learning techniques can also benefit from incorporating structure-preserving ideas to improve their prediction and generalizability.
This PIMS Collaborative Research Group (CRG) on Structure-Preserving Discretizations and their Applications will bring together researchers in structure-preserving discretizations from academia and industry to share their knowledge, expertise, and current challenges. The main three themes of this CRG are:
Development of Structure-Preserving Discretizations
Applications of Structure-Preserving Discretizations
Structure-Preserving Machine Learning Methods
The CRG Organizers consist of members from Simon Fraser University, University of Saskatchewan, University of Washington, and University of California, Merced. This CRG will host various events and long-term visitors to foster collaboration within and beyond the PIMS network, as well mentoring postdoctoral scholars, graduate and undergraduate students.