Weights initialization of neural networks for function approximation

• URL: http://arxiv.org/abs/2510.08780v1
• Date: Thu, 09 Oct 2025 19:56:26 GMT
• Title: Weights initialization of neural networks for function approximation
• Authors: Xinwen Hu, Yunqing Huang, Nianyu Yi, Peimeng Yin,
• Abstract summary: Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning.<n>We propose a reusable framework based on on basis function pretraining.<n>In this approach, basis neural networks are first trained to approximate families of structural correspondences on a reference domain.<n>Their learned parameters are then used to initialize networks for more complex target functions.
• Score: 0.9099663022952497
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new model from scratch; (ii) performance is highly sensitive to architectural and hyperparameter choices; and (iii) models frequently generalize poorly beyond the training domain. To overcome these challenges, we propose a reusable initialization framework based on basis function pretraining. In this approach, basis neural networks are first trained to approximate families of polynomials on a reference domain. Their learned parameters are then used to initialize networks for more complex target functions. To enhance adaptability across arbitrary domains, we further introduce a domain mapping mechanism that transforms inputs into the reference domain, thereby preserving structural correspondence with the pretrained models. Extensive numerical experiments in one- and two-dimensional settings demonstrate substantial improvements in training efficiency, generalization, and model transferability, highlighting the promise of initialization-based strategies for scalable and modular neural function approximation. The full code is made publicly available on Gitee.

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