Solving Partial Differential Equations with Equivariant Extreme Learning Machines
arxiv(2024)
摘要
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 sample efficiency and to enforce equivariance.
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