ExtremONet: Extreme-Learning-based Neural Operator for identifying dynamical systems

Jari Beysen, Floriano Tori
Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", PMLR 277:96-120, 2025.

Abstract

The DeepONet, based on the Universal Approximation Theorem for Operators (UATO), made a significant impact on Deep Learning research due to its ability to learn maps between function spaces instead of between vector spaces like traditional Neural Networks. However, DeepONets are computationally expensive to train. To address this we introduce the ExtremONet: an Extreme-Learning-Machine-based variation of the DeepONet, capable of one-step learning maps between function spaces. We show that ExtremONets approach DeepONets in training error whilst displaying lower generalization error, and training between two to four orders of magnitude faster on small datasets. Our work represents an important step towards efficient dynamical modeling using Machine Learning. We conclude our analysis with an exploration of the ExtremONet’s Out-of-Distribution Generalization capabilities.

Cite this Paper

BibTeX
@InProceedings{pmlr-v277-beysen25a, title = {ExtremONet: Extreme-Learning-based Neural Operator for identifying dynamical systems}, author = {Beysen, Jari and Tori, Floriano}, booktitle = {Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"}, pages = {96--120}, year = {2025}, editor = {Coelho, Cecı́lia and Zimmering, Bernd and Costa, M. Fernanda P. and Ferrás, Luı́s L. and Niggemann, Oliver}, volume = {277}, series = {Proceedings of Machine Learning Research}, month = {26 Oct}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v277/main/assets/beysen25a/beysen25a.pdf}, url = {https://proceedings.mlr.press/v277/beysen25a.html}, abstract = {The DeepONet, based on the Universal Approximation Theorem for Operators (UATO), made a significant impact on Deep Learning research due to its ability to learn maps between function spaces instead of between vector spaces like traditional Neural Networks. However, DeepONets are computationally expensive to train. To address this we introduce the ExtremONet: an Extreme-Learning-Machine-based variation of the DeepONet, capable of one-step learning maps between function spaces. We show that ExtremONets approach DeepONets in training error whilst displaying lower generalization error, and training between two to four orders of magnitude faster on small datasets. Our work represents an important step towards efficient dynamical modeling using Machine Learning. We conclude our analysis with an exploration of the ExtremONet’s Out-of-Distribution Generalization capabilities.} }
Endnote
%0 Conference Paper %T ExtremONet: Extreme-Learning-based Neural Operator for identifying dynamical systems %A Jari Beysen %A Floriano Tori %B Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications" %C Proceedings of Machine Learning Research %D 2025 %E Cecı́lia Coelho %E Bernd Zimmering %E M. Fernanda P. Costa %E Luı́s L. Ferrás %E Oliver Niggemann %F pmlr-v277-beysen25a %I PMLR %P 96--120 %U https://proceedings.mlr.press/v277/beysen25a.html %V 277 %X The DeepONet, based on the Universal Approximation Theorem for Operators (UATO), made a significant impact on Deep Learning research due to its ability to learn maps between function spaces instead of between vector spaces like traditional Neural Networks. However, DeepONets are computationally expensive to train. To address this we introduce the ExtremONet: an Extreme-Learning-Machine-based variation of the DeepONet, capable of one-step learning maps between function spaces. We show that ExtremONets approach DeepONets in training error whilst displaying lower generalization error, and training between two to four orders of magnitude faster on small datasets. Our work represents an important step towards efficient dynamical modeling using Machine Learning. We conclude our analysis with an exploration of the ExtremONet’s Out-of-Distribution Generalization capabilities.
APA
Beysen, J. & Tori, F.. (2025). ExtremONet: Extreme-Learning-based Neural Operator for identifying dynamical systems. Proceedings of the 2nd ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", in Proceedings of Machine Learning Research 277:96-120 Available from https://proceedings.mlr.press/v277/beysen25a.html.

Related Material