arXiv:2605.31027v1 Announce Type: new Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional input, it employs $d$ independent subnetworks -- each acting on a single coordinate -- and constructs basis functions via element-wise multiplication of their outputs. The PDE solution is approximated as a linear combination of these basis functions, wi
The continuous advancements in AI and neural network architectures are leading to more sophisticated methods for solving complex computational problems like PDEs.
This breakthrough could significantly accelerate scientific discovery, engineering design, and simulation across various fields by providing a more efficient way to solve high-frequency PDEs.
Traditional numerical methods for PDEs might be augmented or even supplanted by more accurate and efficient neural network approaches, especially for high-frequency problems.
- · AI/ML researchers
- · Computational scientists
- · Engineering industries
- · Drug discovery platforms
- · Developers of legacy PDE solvers
Faster and more accurate simulations in physics, chemistry, and materials science.
Accelerated development of new technologies and products due to quicker R&D cycles.
Enhanced AI capabilities for real-time decision-making in complex systems, potentially impacting autonomous systems and climate modeling.
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Read at arXiv cs.LG