Solving Partial Differential Equations with Equivariant Extreme Learning Machines
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 19 of its 42 references that are in the map. First posted on arXiv 29 Apr 2024.
Builds on
19 of 42 references.
References · 19
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7 more
- 2023Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learningcited by 21
- 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 16
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- 2021Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamicscited by 10
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- 2023Equivariance and partial observations in Koopman operator theory for partial differential equationscited by 6
- 2023Learning a model is paramount for sample efficiency in reinforcement learning control of PDEscited by 5
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Citing papers per year: 2024: 1; 2025: 1.
2 papers.