analiza aiqbench
This research benchmark evaluates sampling strategies and neural architectures for solving inverse PDE problems in unbounded domains, specifically comparing standard MLPs with Kolmogorov-Arnold Networks (KANs). The study demonstrates that Gaussian and exponential sampling distributions significantly enhance reconstruction accuracy in far-field regions while KANs offer superior efficiency by reducing neuron counts, albeit at a higher computational cost during training. These findings provide critical insights for advancing physics-informed machine learning methods capable of handling infinite domains without artificial truncation.
Evaluation of Sampling Strategies and Physics-Informed Kolmogorov--Arnold Networks in Unbounded Domains
arXiv:2512.12074v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have emerged as an effective approach for solving partial differential equations (PDEs) by incorporating physical laws into the learning process. However, their application to infinite and semi-infinite domains remains challenging due to the difficulty of representing unbounded regions with a finite number of training points. This work evaluates physics-informed learning strategies for inverse PDE problems in unbounded domains, focusing on the influence of sampling strategies based on uniform, Gaussian, and exponential distributions, and on the use of conventional multilayer perceptrons (MLPs) and Kolmogorov--Arnold Networks (KANs) within the PINN framework. The proposed benchmark considers manufactured inverse problems on infinite and semi-infinite domains, enabling quantitative assessment of reconstruction accuracy and computational efficiency. Results show that Gaussian and exponential sampling, controlled through explicit distribution parameters, improve reconstruction accuracy in the far field and offer a direct mechanism for embedding problem-specific prior knowledge into training. PIKANs, whose edge-based functional representation is grounded in the Kolmogorov--Arnold representation theorem, match or exceed the accuracy of MLP-based PINNs while requiring fewer neurons, though their spline-based formulation increases the computational cost of training, inference, and derivative evaluation.
Abstract:Physics-informed neural networks (PINNs) have emerged as an effective approach for solving partial differential equations (PDEs) by incorporating physical laws into the learning process. However, their application to infinite and semi-infinite domains remains challenging due to the difficulty of representing unbounded regions with a finite number of training points. This work evaluates physics-informed learning strategies for inverse PDE problems in unbounded domains, focusing on the influence of sampling strategies based on uniform, Gaussian, and exponential distributions, and on the use of conventional multilayer perceptrons (MLPs) and Kolmogorov--Arnold Networks (KANs) within the PINN framework. The proposed benchmark considers manufactured inverse problems on infinite and semi-infinite domains, enabling quantitative assessment of reconstruction accuracy and computational efficiency. Results show that Gaussian and exponential sampling, controlled through explicit distribution parameters, improve reconstruction accuracy in the far field and offer a direct mechanism for embedding problem-specific prior knowledge into training. PIKANs, whose edge-based functional representation is grounded in the Kolmogorov--Arnold representation theorem, match or exceed the accuracy of MLP-based PINNs while requiring fewer neurons, though their spline-based formulation increases the computational cost of training, inference, and derivative evaluation.
Machine Learning (cs.LG); Mathematical Physics (math-ph)
arXiv:2512.12074 [cs.LG]
(or arXiv:2512.12074v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2512.12074 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 278 cuvinte
Subiecte conexe
A Mike's-Eye View of ARC's Research
AI Alignment Forum · 9 iun. 2026
Informe de riesgos de la IA de frontera (febrero–marzo de 2026)
METR · 19 mai 2026
Frontier AI Risk Report (February–March 2026)
METR · 19 mai 2026
Frontier Risk Report (February to March 2026)
METR · 19 mai 2026