PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function
Summary
PIKFNO is a new interpretable neural operator framework that integrates physics-informed kernel functions from governing equations to enhance predictive accuracy and interpretability with limited training data.
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# PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function Source: [https://arxiv.org/abs/2608.14619](https://arxiv.org/abs/2608.14619) [View PDF](https://arxiv.org/pdf/2608.14619) > Abstract:This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator \(PIKFNO\), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture\. Unlike traditional neural operators such as DeepONet, which rely on deep networks to implicitly learn basis functions, PIKFNO constrains the trunk network through physics informed kernel functions, thereby aligning its operator structure with the kernel expansions used in meshless collocation methods\. Two construction strategies are introduced: one learns kernel functions directly from data, where the learned kernel can be regarded as a nonsingular fundamental solution, while the other builds them through transformations of analytical fundamental solutions\. Numerical experiments demonstrate that PIKFNO achieves high predictive accuracy with substantially improved interpretability and superior generalization under limited training data\. The proposed framework offers a new pathway for developing efficient, physically consistent, and interpretable neural operators\. ## Submission history From: Zhuojia Fu Prof\. \[[view email](https://arxiv.org/show-email/b6aed9a6/2608.14619)\] **\[v1\]**Sat, 11 Jul 2026 19:08:05 UTC \(614 KB\)
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