arXiv:2410.04096v2 Announce Type: replace Abstract: In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to Multilayer Perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to effectively represent both smooth functions and functions with singularities. This is important not only for function approximation but also for sol
The continuous exploration of novel architectures and activation functions in AI, particularly for addressing foundational scientific computing challenges, drives the emergence of methods like Sinc Kolmogorov-Arnold Networks.
Improving the ability of neural networks to accurately model complex functions, especially those with singularities, directly impacts the efficacy of AI in scientific discovery, engineering, and the solution of real-world physical problems.
The introduction of Sinc interpolation to Kolmogorov-Arnold Networks provides a potentially more robust and efficient method for solving partial differential equations, which are fundamental to many scientific and engineering domains.
- · AI researchers
- · Computational scientists
- · Engineering R&D sectors
- · Physics research
- · Traditional numerical methods (potentially)
Scientific fields reliant on solving complex PDEs will see enhanced simulation and modeling capabilities.
Faster and more accurate solutions for problems in material science, fluid dynamics, and climate modeling could accelerate innovation.
The broader adoption of such AI-driven solvers could reduce the cost and time of R&D in various industries, leading to new product development cycles.
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Read at arXiv cs.LG