Neural Networks, Differential Equations, and Structure Preservation
Has parts
Paper 1: Celledoni, Elena; Murari, Davide; Owren, Brynjulf Rustad; Schonlieb, Carola-Bibiane; Sherry, Ferdia. Dynamical Systems - Based Neural Networks. SIAM Journal on Scientific Computing 2023 ;Volum 45.(6) s. A3071-A3094. Published by Society for Industrial and Applied Mathematics. Available at: http://dx.doi.org/10.1137/22M1527337Paper 2: Eliasof, Moshe; Murari, Davide; Schönlieb, Carola-Bibiane; Sherry, Ferdia. Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach. Available at: https://doi.org/10.48550/arXiv.2311.06942
Paper 3: Celledoni, Elena; Jackaman, James, Murari, Davide; Owren, Brynjulf. Predictions Based on Pixel Data: Insights from PDEs and Finite Differences. Available at: https://doi.org/10.48550/arXiv.2305.00723
Paper 4: Celledoni, Elena; Çokaj, Ergys; Leone, Andrea; Murari, Davide; Owren, Brynjulf. Lie Group integrators for mechanical systems. International Journal of Computer Mathematics 2021 s. 58-88. Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons CC BY-NC-ND. Available at http://dx.doi.org/10.1080/00207160.2021.1966772
Paper 5: Celledoni, Elena; Leone, Andrea; Murari, Davide; Owren, Brynjulf. Learning Hamiltonians of constrained mechanical systems. Journal of Computational and Applied Mathematics 2022 ;Volum 417. s. - Published by Elsevier B.V. This is an open access article under the CC BY license http://dx.doi.org/10.1016/j.cam.2022.114608
Paper 6: Celledoni, Elena; Çokaj, Ergys; Leone, Andrea; Leyendecker, Sigrid; Owren, Brynjulf; de Almagro, Rodrigo T. Sato Martín; Stavole, Martina. Neural networks for the approximation of Euler’s elastica. https://doi.org/10.48550/arXiv.2312.00644
Paper 7: Betcke, Marta; Kreusser, Lisa Maria; Murari, Davide. Parallel-in-Time Solutions with Extreme Learning Machines. Preprint.