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We utilize extreme learning machines for the prediction of partial differential equations (PDEs). Our method splits the computational domain 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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Solving Partial Differential Equations with Equivariant Extreme Learning Machines

  • 会议论文

  • 发表日期：

    2025年

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  • Hans Harder,
  • Jean Rabault,
  • Ricardo Vinuesa,
  • Mikael Mortensen,
  • Sebastian Peitz

摘要

We utilize extreme learning machines for the prediction of partial differential equations (PDEs). Our method splits the computational domain 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.