Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs
arXiv:2601.00672v2 Announce Type: replace-cross Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs, SIAM J. Sci. Comput., 47(2), C501-C528, 2025. FEONet realizes the parameter-to-solution map on a finite element space and admits a training procedure that does not require training data, while exhibiting high accuracy and robustness across a broad class of problems. However, its computat
The continuous pursuit of more efficient and less resource-intensive AI models for complex scientific and engineering problems makes advancements in operator networks pertinent now.
This development proposes a more efficient method for solving parametric partial differential equations (PDEs) without extensive training data, reducing computational and memory costs for scientific machine learning applications.
The introduction of Sparse FEONet allows for high accuracy and robustness in solving PDEs with significantly lower computational and memory requirements compared to previous methods, enabling broader application of operator networks.
- · Scientific computing researchers
- · Engineering design firms
- · AI hardware developers
- · Cloud computing providers
- · Traditional high-cost simulation software vendors
Reduced computational burden for complex simulations and scientific machine learning tasks.
Accelerated discovery and design cycles across various scientific and engineering disciplines due to faster, cheaper simulations.
Democratization of advanced simulation capabilities, lowering barriers to entry for research and development in fields requiring PDE solutions.
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