Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics

D Millard, A Carr, S Gaudreault - arXiv preprint arXiv:2409.06522, 2024 - arxiv.org
Deep learning is revolutionizing weather forecasting, with new data-driven models
achieving accuracy on par with operational physical models for medium-term predictions …

Low-synchronization Arnoldi Methods for the Matrix Exponential with Application to Exponential Integrators

T Tafolla, S Gaudreault, M Tokman - arXiv preprint arXiv:2410.14917, 2024 - arxiv.org
High order exponential integrators require computing linear combination of exponential like
$\varphi $-functions of large matrices $ A $ times a vector $ v $. Krylov projection methods …

Optimization of Approximate Maps for Linear Systems Arising in Discretized PDEs

R Islam, A Carr, C Jacobs - arXiv preprint arXiv:2406.17656, 2024 - arxiv.org
Generally, discretization of partial differential equations (PDEs) creates a sequence of linear
systems $ A_k x_k= b_k, k= 0, 1, 2,..., N $ with well-known and structured sparsity patterns …