7 papers
Zero-shot generalization of transformer neural operators to larger domains
Armand de Villeroché, Sibo Cheng, Vincent Le Guen +5
Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing…
Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder
Kewei Zhu, Yanze Xin, Jinwei Hu +3
Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing…
Information Shapes Koopman Representation
Xiaoyuan Cheng, Wenxuan Yuan, Yiming Yang +4
The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dime…
Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators
Xiao Xue, Marco F. P. ten Eikelder, Mingyang Gao +7
The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle di…
Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation
Yiming Yang, Xiaoyuan Cheng, Daniel Giles +5
Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensio…
Learning Chaos In A Linear Way
Xiaoyuan Cheng, Yi He, Yiming Yang +5
Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. The…