Learning Semilinear Neural Operators : A Unified Recursive Framework For Prediction And Data Assimilation

arXiv:2402.15656v1 Announce Type: new
Abstract: Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely …

abstract advances arxiv challenges complex systems computation cs.ai cs.lg cs.na current data differential face framework math.na operators prediction recursive solutions success systems temporal theory type