Grunnleggende konsepter
A learning-based state-space approach for semilinear PDEs enables efficient prediction and data assimilation.
Sammendrag
Recent advances in Neural Operators (NOs) have led to fast and accurate solutions for complex systems described by partial differential equations (PDEs). However, challenges arise with spatio-temporal PDEs over long time scales due to the lack of a systematic framework for data assimilation. The proposed framework, NODA, combines prediction and correction operations to handle irregularly sampled noisy measurements efficiently. Extensive experiments on various equations demonstrate the robustness of NODA in predicting trajectories accurately over long horizons and assimilating data effectively.
Statistikk
Published as a conference paper at ICLR 2024
Department of Electrical and Computer Engineering, Northeastern University, Boston MA, 02115, USA.
CNRS, CRAN, Université de Lorraine, Vandoeuvre-lès-Nancy, F-54000 Nancy, France.
Institute for Experiential AI, Northeastern University, Boston MA, 02115, USA.
arXiv:2402.15656v2 [cs.LG] 15 Mar 2024
Sitater
"We propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs."
"The resulting method is capable of producing fast and accurate predictions over long time horizons."
"NODA leads to better prediction performance compared with other closely related NO approaches."
"The contributions of this work extend the NO theory by leveraging the observer design of semilinear PDEs."
"The resulting framework can estimate solutions using arbitrary amounts of measurements."