Solving Partial Differential Equations with Equivariant Extreme Learning Machines

2024/04/29 by H. Harder, Harder, Hans, Rabault, Jean +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and ELM

paper · pdf · doi:10.48550/arxiv.2404.18530

openalex publication_date 2024/04/29 · openalex created_date 2024/05/02 · openalex updated_date 2026/07/28

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.

Cited by

• Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders

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