Elena Celledoni

Elena Celledoni is a Professor in the Department of Mathematical Sciences at the Norwegian University of Science and Technology (NTNU). She has been employed at NTNU since 2004 and has held the position of professor since 2009. She is a member of the Differential Equations and Numerical Analysis Group at the Department of Mathematical Sciences and serves as its leader.

Her educational background includes:

• Master's degree in Mathematics from the University of Trieste (1993)
• Ph.D. in Computational Mathematics from the University of Padua, Italy (1997)

Elena Celledoni's research focuses on numerical analysis, particularly structure preserving algorithms for differential equations and geometric numerical integration. Her work bridges theoretical mathematics with practical computational methods, developing algorithms that maintain the geometric properties of the systems they approximate. She has made significant contributions to Lie group integrators, energy-preserving methods, and the application of these techniques to mechanical systems and shape analysis. In recent years, her research has expanded to include the intersection of numerical methods with machine learning, exploring how structure-preserving approaches can enhance neural networks and data-driven modeling.

Her publications demonstrate a clear trend toward integrating traditional numerical analysis with modern machine learning techniques while maintaining a strong foundation in geometric integration and structure preservation. This interdisciplinary approach has led to innovations in neural ODEs, structure-preserving neural networks, and physics-informed machine learning models that respect the underlying mathematical structures of the systems they model.

Elena Celledoni has received recognition for her work through the following honors:

• Member of the Royal Norwegian Society of Sciences and Letters
• Member of the European Consortium of Mathematics in Industry Council
• Member of the board of the International Council of Mathematics in Industry and Applications
• Editorial board member for SIAM Review, Journal of Computational Dynamics, Journal of Geometric Mechanics, Calcolo, and Networks and Heterogeneous Media

As an advisor, she has mentored several students including Torbjørn Ringholm who completed his doctoral dissertation on 'Discrete gradient methods in image processing and partial differential equations on moving meshes.' Her research has been supported by various grants enabling her to lead projects on geometric numerical integration, collaborate internationally, and organize significant academic events such as the special semester at Isaac Newton Institute of MS in 2019 on 'Geometry, compatibility and structure preservation.'

She leads the Differential Equations and Numerical Analysis Group at NTNU, which focuses on developing and analyzing numerical methods that preserve the geometric structure of differential equations. The group maintains active collaborations with researchers worldwide and has made substantial contributions to advancing the field of geometric numerical integration and its applications to real-world problems.