Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling

arXiv:2401.09516v2 Announce Type: replace
Abstract: Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in …

abstract arxiv attention cs.ai cs.lg cs.na data differential efficiency however inference math.na operators process recycling solutions together training type via