Solving partial differential equations with equivariant extreme learning machines
H. Harder, S. Peitz, in: J. Berberich, A. Ianelli, F. Allgöwer (Eds.), Systems Theory in Data and Optimization, Springer, Cham, 2025, pp. 153–168.
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Editor
Berberich, J.;
Ianelli, A.;
Allgöwer, F.
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 sample efficiency and to enforce equivariance.
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Systems theory in data and optimization
Page
153-168
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Harder H, Peitz S. Solving partial differential equations with equivariant extreme learning machines. In: Berberich J, Ianelli A, Allgöwer F, eds. Systems Theory in Data and Optimization. Springer; 2025:153-168. doi:10.1007/978-3-031-83191-1_10
Harder, H., & Peitz, S. (2025). Solving partial differential equations with equivariant extreme learning machines. In J. Berberich, A. Ianelli, & F. Allgöwer (Eds.), Systems theory in data and optimization (pp. 153–168). Springer. https://doi.org/10.1007/978-3-031-83191-1_10
@inproceedings{Harder_Peitz_2025, place={Cham}, title={Solving partial differential equations with equivariant extreme learning machines}, DOI={10.1007/978-3-031-83191-1_10}, booktitle={Systems theory in data and optimization}, publisher={Springer}, author={Harder, Hans and Peitz, Sebastian}, editor={Berberich, J. and Ianelli, A. and Allgöwer, F.}, year={2025}, pages={153–168} }
Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations with Equivariant Extreme Learning Machines.” In Systems Theory in Data and Optimization, edited by J. Berberich, A. Ianelli, and F. Allgöwer, 153–68. Cham: Springer, 2025. https://doi.org/10.1007/978-3-031-83191-1_10.
H. Harder and S. Peitz, “Solving partial differential equations with equivariant extreme learning machines,” in Systems theory in data and optimization, 2025, pp. 153–168, doi: 10.1007/978-3-031-83191-1_10.
Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations with Equivariant Extreme Learning Machines.” Systems Theory in Data and Optimization, edited by J. Berberich et al., Springer, 2025, pp. 153–68, doi:10.1007/978-3-031-83191-1_10.
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