Uncertainty Quantification with Bayesian Higher Order ReLU KANs

James Giroux, Cristiano Fanelli
10/2/2024
cs.LGcs.AIphysics.data-an

Official code: wmdataphys/Bayesian-HR-KAN (8 stars, last commit 2024-10-03).

Abstract

We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs to enhance computational efficiency given the computational demands of Bayesian methods. The method we propose is general in nature, providing access to both epistemic and aleatoric uncertainties. It is also capable of generalization to other various basis functions. We validate our method through a series of closure tests, including simple one-dimensional functions and application to the domain of (Stochastic) Partial Differential Equations. Referring to the latter, we demonstrate the method's ability to correctly identify functional dependencies introduced through the inclusion of a stochastic term. The code supporting this work can be found at https://github.com/wmdataphys/Bayesian-HR-KAN

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Code Implementations(1)

wmdataphys/Bayesian-HR-KANOfficial100%

Bayesian (Higher Order) ReLU-KANs

80Python, Jupyter NotebookSep 12, 20242 years ago

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Cite this paper

@article{giroux2024uncertainty,
  title  = {Uncertainty Quantification with Bayesian Higher Order ReLU KANs},
  author = {James Giroux and Cristiano Fanelli},
  year   = {2024},
  eprint = {2410.01687},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2410.01687v2}
}

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