AttNS: Attention-Inspired Numerical Solving For Limited Data Scenarios

Zhongzhan Huang, Mingfu Liang, Shanshan Zhong, Liang Lin
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:19929-19948, 2024.

Abstract

We propose the attention-inspired numerical solver (AttNS), a concise method that helps the generalization and robustness issues faced by the AI-Hybrid numerical solver in solving differential equations due to limited data. AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness for conventional deep learning tasks. Drawing from the dynamical system perspective of ResNet, We seamlessly incorporate attention mechanisms into the design of numerical methods tailored for the characteristics of solving differential equations. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, showcase AttNS consistently enhancing various numerical solvers without any intricate model crafting. Finally, we analyze AttNS experimentally and theoretically, demonstrating its ability to achieve strong generalization and robustness while ensuring the convergence of the solver. This includes requiring less data compared to other advanced methods to achieve comparable generalization errors and better prevention of numerical explosion issues when solving differential equations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-huang24m, title = {{A}tt{NS}: Attention-Inspired Numerical Solving For Limited Data Scenarios}, author = {Huang, Zhongzhan and Liang, Mingfu and Zhong, Shanshan and Lin, Liang}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {19929--19948}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/huang24m/huang24m.pdf}, url = {https://proceedings.mlr.press/v235/huang24m.html}, abstract = {We propose the attention-inspired numerical solver (AttNS), a concise method that helps the generalization and robustness issues faced by the AI-Hybrid numerical solver in solving differential equations due to limited data. AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness for conventional deep learning tasks. Drawing from the dynamical system perspective of ResNet, We seamlessly incorporate attention mechanisms into the design of numerical methods tailored for the characteristics of solving differential equations. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, showcase AttNS consistently enhancing various numerical solvers without any intricate model crafting. Finally, we analyze AttNS experimentally and theoretically, demonstrating its ability to achieve strong generalization and robustness while ensuring the convergence of the solver. This includes requiring less data compared to other advanced methods to achieve comparable generalization errors and better prevention of numerical explosion issues when solving differential equations.} }
Endnote
%0 Conference Paper %T AttNS: Attention-Inspired Numerical Solving For Limited Data Scenarios %A Zhongzhan Huang %A Mingfu Liang %A Shanshan Zhong %A Liang Lin %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-huang24m %I PMLR %P 19929--19948 %U https://proceedings.mlr.press/v235/huang24m.html %V 235 %X We propose the attention-inspired numerical solver (AttNS), a concise method that helps the generalization and robustness issues faced by the AI-Hybrid numerical solver in solving differential equations due to limited data. AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness for conventional deep learning tasks. Drawing from the dynamical system perspective of ResNet, We seamlessly incorporate attention mechanisms into the design of numerical methods tailored for the characteristics of solving differential equations. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, showcase AttNS consistently enhancing various numerical solvers without any intricate model crafting. Finally, we analyze AttNS experimentally and theoretically, demonstrating its ability to achieve strong generalization and robustness while ensuring the convergence of the solver. This includes requiring less data compared to other advanced methods to achieve comparable generalization errors and better prevention of numerical explosion issues when solving differential equations.
APA
Huang, Z., Liang, M., Zhong, S. & Lin, L.. (2024). AttNS: Attention-Inspired Numerical Solving For Limited Data Scenarios. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:19929-19948 Available from https://proceedings.mlr.press/v235/huang24m.html.

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