Predicting PDEs Fast and Efficiently with Equivariant Extreme Learning Machines

arXiv:2404.18530v1 Announce Type: new
Abstract: We utilize extreme learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase …

abstract arxiv cases cs.lg data differential learn machines multiple prediction space state type windows