arXiv:2512.09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk network, which operates directly on raw spatial or spatiotemporal coordinates through fully connected layers, often struggles to represent sharp gradients, boundary layers, and other non-periodic solution structures on bounded domains. To address these limitations, we introduce the Spectral-Embedded Deep Oper
The continuous drive to improve deep learning's ability to model complex physical phenomena with greater accuracy and robustness is pushing research into advanced architectural enhancements for operator networks.
This development proposes a method to significantly enhance the accuracy and robustness of DeepONets, particularly in scenarios involving sharp gradients and non-periodic structures, which is critical for reliable scientific machine learning.
DeepONets could become more reliable and broadly applicable for solving complex PDEs and simulating physical systems, reducing the need for traditional numerical methods in certain applications.
- · Scientific machine learning researchers
- · Engineering simulation software developers
- · Industries relying on physical modeling (e.g., aerospace, energy)
- · Traditional numerical methods that DeepONets might increasingly replace
Improved DeepONet performance for systems with challenging features like shocks or boundary layers.
Faster and more accurate data-driven solutions to previously intractable or computationally expensive PDE problems.
Acceleration of research and development cycles in areas from materials science to climate modeling due to enhanced simulation capabilities.
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Read at arXiv cs.LG