Solving Partial Differential Equations with Equivariant Extreme Learning Machines
This addresses efficient PDE prediction for computational science, but it is incremental as it builds on existing extreme-learning machine methods.
The paper tackles predicting partial differential equations (PDEs) using extreme-learning machines by splitting the state space into windows and exploiting symmetries, achieving high accuracy and long-term predictions with few data points, such as learning from a single snapshot.
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.